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latex_slides_beamer_example/README 0000640 0001750 0001750 00000000712 12217057167 016034 0 ustar lada lada Files:
1. source file with text: slides.tex
2. Figures: in the directory 'figures'
3. References: in file 'bibfil.bib'
***
1. Compile the document and create a PDF file
latex slides; dvips -o slides.ps slides
1b. if you want to turn it into a PDF file type
ps2pdf example.ps
2. If you have added any new references (with the commande \cite) run
bibtex slides
and re-compile twice
3. View the file with, for example, evince, xpdf or acroread
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Pretend that you're Hercule Poirot: Examine all clues,
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@string{prsoc = "Philos. Trans. Roy. Soc."}
@string{rsoc = "Proc. Roy. Soc."}
@string{theor = "Theoretical and Computational Fluid Dynamics"}
@string{nhtb = "Numerical Heat Transfer. Part B"}
@string{nhta = "Numerical Heat Transfer. Part A"}
@string{arfm = "Annual Review of Fluid Mechanics"}
@string{arfms = "Ann. Rev. Fluid Mech."}
@string{jfm = "Journal of Fluid Mechanics"}
@string{jfms = "J. Fluid Mech."}
@string{ihmt = "International Journal of Heat and Mass Transfer"}
@string{ijnmf = "International Journal for Numerical Methods in Fluids"}
@string{ihmts = "Int. J. Heat Mass Transfer"}
@string{ijnmhff = "International Journal for Numerical Methods in Fluids"}
@string{arfm = "Annual Review of Fluid Mechanics"}
@string{aiaa = "{AIAA} Journal"}
@string{pha = "Physics of Fluids A"}
@string{ph = "Physics of Fluids"}
@string{phb = "Physics of Fluids B"}
@string{ph = "Physics of Fluids"}
@string{jot = "Journal of Turbulence"}
@string{pfas = "Phys. Fluids A"}
@string{pfa = "Physics of Fluids A"}
@string{cmame = "Computer Methods in Applied Mechanics and Engineering"}
@string{cmames = "Comp. Meth. Appl. Mech. \& Eng."}
@string{jwes = "Journal of Wind Engineering and Industrial Aerodynamics"}
@string{cfluid = "Computers {\&} Fluids"}
@string{mphasec= "International Journal of Multiphase Flow"}
@string{numha = "Numerical Heat Transfer, Part A"}
@string{turbo = "Journal of Turbomachinery"}
@string{jcphys = "Journal of Computational Physics"}
@string{jam = "Trans. {ASME}: J. Appl. Mech."}
@string{jfe = "Journal of Fluids Engineering"}
@string{basic = "Trans. {ASME}: J. Basic Engng"}
@string{jht = "Journal of Heat Transfer"}
@string{jasa = "J. Acoust. Soc. Am"}
@string{expf = "Experiments in Fluids"}
@string{etfs = "Experimental Thermal and Fluid Science"}
@string{exptfs = "Exp. Thermal \& Fluid Science"}
@string{jfs = "Journal of Fluids and Structures"}
@string{jfss = "J. Fluids \& Struct."}
@string{jsmeb = "{JSME} International Journal, Series B"}
@string{jsmebs = "{JSME} Int. J., Ser. B"}
@string{eurb = "Eur. J. Mech., {B}/{F}luids"}
@string{asce = "Trans. {ASCE}: J. Engng. Mech. Div."}
@string{asceh = "Trans. {ASCE}: J. Hydraulics Div."}
@string{ascen = "Trans. {ASCE}: J. Engng. Mech."}
@string{jem = "Journal of Engineering Mathematics"}
@string{ijhff = "International Journal of Heat and Fluid Flow"}
@string{atm = "Atmospheric Environment"}
@string{qmr = "Quarterly Journal of Royal Meteorological Society"}
@string{ftac = "Flow, Turbulence and Combustion"}
@string{caf = "Computers \& Fluids"}
@InProceedings{atilla-raodtolls,
author="Alt{\i}nta{\c{s}}, Atilla
and Davidson, Lars",
editor="Martins, Ana L{\'u}cia
and Ferreira, Jo{\~a}o C.
and Kocian, Alexander
and Costa, Vera",
title="{EMD-SVR}: A Hybrid Machine Learning Method to Improve the Forecasting Accuracy of Highway Tollgates Traveling Time to Improve the Road Safety",
booktitle="Intelligent Transport Systems, From Research and Development to the Market Uptake",
year="2021",
publisher="Springer International Publishing",
address="Cham",
pages="241--251",
isbn="978-3-030-71454-3"
}
@article{sillero:13,
annote = "",
author = "J.A. Sillero and J. Jimenez and R.D. Moser",
title = "One-point statistics for turbulent wall-bounded flows at {Reynolds} numbers up to $\delta^+\simeq 2000$",
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year = 2014}
@incollection{hump:go4hybrid:18,
annote = "",
author = "A. Garbaruk and E. Guseva and M. Shur and M. Strelets and A. Travin ",
title = "{2D} Wall-Mounted Hump",
booktitle = "Go4Hybrid: Grey Area Mitigation for Hybrid RANS-LES Methods",
series = "Notes on Numerical Fluid Mechanics and Multidisciplinary Design",
publisher = "Springer Verlag",
editor ="Charles Mockett and Werner Haase and Dieter Schwamborn",
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volume=134,
year = 2018 }
@MISC{pyamg,
author = "Olson, L. N. and Schroder, J. B.",
title = "{PyAMG}: Algebraic Multigrid Solvers in {Python} v4.0",
year = "2018",
url = "https://github.com/pyamg/pyamg",
note = "Release 4.0"
}
@inproceedings{davidson:21,
title={ Detached Eddy Simulation coupled with steady {RANS} in the wall region\href{http://www.tfd.chalmers.se/~lada/postscript_files/etmm13-sdes.pdf}{\faIcon{external-link-alt}}},
author={Davidson, L.},
booktitle={13th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM13), Rhodes/Digital,
Greece 15-17 September},
year={2021}
}
@inproceedings{davidson-friess:21,
title={Detached Eddy Simulations: Analysis of a limit on the dissipation term for reducing spectral
energy transfer at cut-off\href{http://www.tfd.chalmers.se/~lada/postscript_files/paper-iddes-pc-etmm13.pdf}{\faIcon{external-link-alt}}},
author={Davidson, L. and Friess, C.},
booktitle={13th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM13), Rhodes/Digital,
Greece 15-17 September},
year={2021}
}
@incollection{davidson:19a,
author = "L. Davidson",
title = "Non-Zonal Detached Eddy Simulation coupled with a steady {RANS} solver in the wall region",
booktitle = "Special Issue on \emph{Current trends in RANS-based scale-resolving simulation methods}",
series = "ERCOFTAC Bullentin",
pages="43--48",
volume=120,
year = 2019}
@misc{larsson_privat:19,
annote = "",
author = "J. Larsson",
title = "private communication",
howpublished= "Department of Mechanical Engineering, University of Maryland",
address ="College Park, MD, USA",
year = 2019 }
@article{rasam:wallin:17,
author = "Rasam, A. and Wallin, S. and Brethouwer, G. and Johansson, A.V.",
title ="Improving separated-flow predictions using an anisotropy-capturing subgrid-scale model",
journal = ijhff,
volume = 65,
pages = "246--251",
year = 2017 }
@article{backar:17,
author = "J.-A. B{\"a}ckar and L. Davidson",
title = "Evaluation of numerical wall functions on the axisymmetric impinging jet using {OpenFOAM}",
journal = ijhff,
volume = 67,
pages = "27--42",
year = 2017 }
@article{friess-davidson:20,
author = "C. Friess and L. Davidson",
title ="A formulation of {PANS} able to mimic {IDDES}",
url="https://doi.org/10.1016/j.ijheatfluidflow.2020.108666",
journal = ijhff,
number=108666,
volume = 86,
year = 2020 }
@article{davidson-friess:19,
author = "L. Davidson and C. Friess",
title ="A new formulation of $f_k$ for the {PANS} model",
journal = jot,
pages = "1--15",
doi={10.1080/14685248.2019.1641605},
url="http://dx.doi.org/10.1080/14685248.2019.1641605",
year = 2019 }
@article{nguyen-laurence:19,
author = "P.T.L. Nguyen and J.C. Uribe and I. Afgan and D.R. Laurence",
title="A Dual-Grid Hybrid {RANS/LES} Model for Under-Resolved Near-Wall Regions and
its Application to Heated and Separating Flows",
journal=ftac,
volume= 104,
pages = "835--859",
year= 2020,
url="https://doi.org/10.1007/s10494-019-00070-8",
}
@article{shumann:97,
author = "U. Schumann",
title="Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli",
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number=4,
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year=1975}
@article{breuer:schmidt:14,
author= "M. Breuer and S. Schmidt",
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volume=14,
pages = "647--650",
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year=2014}
@inproceedings{davidson:2019,
annote = "",
author = "L. Davidson",
title = "Zonal Detached Eddy Simulation coupled with steady {RANS} in the wall region",
booktitle = "ECCOMAS MSF 2019 Thematic Confernence, Minisyposium ``Current trends in simulation and modelling of turbulent flows. MS devoted to 80th birthday of Prof. Kemo Hanjalic''",
address ="Sarajevo, Bosnia and Herzegovina",
year = 2019}
@article{nebenfuhr_2014c,
year={2015},
issn={0006-8314},
journal={Boundary-Layer Meteorology},
doi={10.1007/s10546-015-0025-9},
title={Large-Eddy Simulation Study of Thermally Stratified Canopy Flow},
url={http://dx.doi.org/10.1007/s10546-015-0025-9},
publisher={Springer Netherlands},
keywords={Atmospheric boundary layer; Forest canopy; Forest turbulence; Large-eddy simulation; Thermal stratification; Turbulent kinetic energy budget},
author={Nebenf{\"u}hr, Bastian and Davidson, Lars},
pages={1-24},
language={English}
}
@article {johan:15,
year={2015},
author = {Arnqvist, J. and Segalini, A. and Dellwik, E. and et al.},
title = {Wind Statistics from a Forested Landscape},
journal={Boundary-Layer Meteorology},
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publisher={Springer Netherlands},
volume=156,
pages={53-71},
}
@article{larsson:17,
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@article{tunstall:17,
author = "R. Tunstall and D. Laurence and R. Prosser and A. Skillen",
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improved consistency",
volume=157,
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journal = caf,
year = 2017 }
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@article{manceau:15,
annote = "",
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generation in large eddy simulation and hybrid {RANS/LES} modeling",
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volume =27,
number =035115,
year = 2015}
@article{deck:14,
annote = "",
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eveloping flat plate turbulent boundary layer over the
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year = 2014}
@techreport{calc-les,
annote = "BER",
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institution = "Division of Fluid Dynamics, Dept. of Mechanics and Maritime Sciences,
Chalmers University of Technology{,} Gothenburg",
year = 2018 }
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pages="629--649",
year = 2014 }
@article{mason:brown:99,
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},
eprint = {
https://doi.org/10.1175/1520-0469(1999)056<2101:OSMAFO>2.0.CO;2
}
}
@techreport{mohammad:06,
annote = "" ,
author = "M. Irannezhad",
title="{DNS} of Channel Flow with Finite Difference Method on a Staggered Grid",
institution = "Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "MSc Thesis",
year = 2006,
}
@techreport{ayyoos:12,
annote = "" ,
author = "A. Zarmehri",
title="Aerodynamic Analysis of wind turbine",
institution = "Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
number = "2012:58",
type = "MSc Thesis",
year = 2012,
}
@techreport{SF:part1,
annote = "",
author = "M. Ekh",
title= "Mechanics of solids \& Fluids -- Introduction to continuum mechanics",
institution = "Div. of Material and Computational Mechanics, Dept. of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Report",
year = 2017,
}
@techreport{SF:part1_old,
annote = "",
author = "S. Toll and M. Ekh",
title= "Mechanics of solids \& Fluids. {P}art {I}: Fundamentals",
institution = "Div. of Material and Computational Mechanics, Dept. of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Report",
year = 2016,}
@misc{wallin:17,
annote = "",
author = "S. Wallin",
title = "private communication",
howpublished= "Dept. of Mechanics, KTH",
address ="Stockholm, Sweden",
year = 2017 }
@article{moser:15,
title={Direct numerical simulation of turbulent channel flow up to $\mathit{Re}_{{\it\tau}}\approx 5200$},
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publisher={Cambridge University Press},
author={Lee, M. and Moser, R. D.},
year={2015},
pages={395--415}}
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document_type={Article},
source={Scopus},
}
@article {WE:WE2076,
author = {Nebenf{\"u}hr, B. and Davidson, L.},
title = {Prediction of wind-turbine fatigue loads in forest regions based on turbulent LES inflow fields},
journal = {Wind Energy},
publisher = {John Wiley \& Sons, Ltd},
issn = {1099-1824},
url = {http://dx.doi.org/10.1002/we.2076},
doi = {10.1002/we.2076},
keywords = {fatigue loads, wind turbine, forest canopy, large-eddy simulation, atmospheric turbulence},
year = {2016},
note = {we.2076},
}
@article{davidson:17,
author = "L. Davidson",
title ="Two-equation hybrid {RANS-LES} models: A novel way to treat $k$ and $\omega$ at inlets and at embedded interfaces",
journal = jot,
volume=18,
number=4,
pages = "291--315",
doi={10.1080/14685248.2017.1281417},
url="http://dx.doi.org/10.1080/14685248.2017.1281417",
year = 2017 }
@Article{atills:16,
author="Alt{\i}nta{\c{s}}, A.
and Davidson, L.",
title="Direct numerical simulation analysis of spanwise oscillating Lorentz force in turbulent channel flow at low Reynolds number",
journal="Acta Mechanica",
year="2016",
pages="1--18",
issn="1619-6937",
doi="10.1007/s00707-016-1754-7",
url="http://dx.doi.org/10.1007/s00707-016-1754-7"
}
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@article{zhang:12,
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year = 2012 }
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author = "Nicoud, Franck and Toda, Hubert Baya and Cabrit, Olivier and Bose, Sanjeeb and Lee, Jungil",
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year = "2011",
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@article{chauvet:deck:07,
author = "N. Chauvet and S. Deck and L. Jacquin",
title = "Zonal Detached Eddy Simulation of a Controlled Propulsive Jet",
journal = aiaa,
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%doi={10.2514/1.28562}.
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year = 2005 }
@article{deck:05b,
author = "S. Deck",
title ="Zonal Detached Eddy Simulation of the Flow Around a High-Lift Configuration",
journal = aiaa,
volume="43",
number =11,
pages ="2372--2384",
year = 2005 }
@techreport{kok:12,
annote = "" ,
author = "J.C. Kok and H. van der Ven",
title = "Capturing free shear layers in hybrid {RANS-LES}
simulations of separated flow",
institution = "National Aerospace Laboratory NLR",
address ="Stockholm",
type = "{NLR-TP-2012-333}",
year = 2012}
@article{davidson:15a,
author = "L. Davidson",
title ="Zonal {PANS}: evaluation of different treatments of the {RANS-LES} interface",
journal = jot,
volume=17,
number=3,
url={http://dx.doi.org/10.1080/14685248.2015.1093637},
pages="274--307",
year = 2016 }
@inproceedings{poitiers,
title={ Evaluation of the time-resolved EHD force produced by a plasma actuator by particle image velocimetry -- a parametric study},
author={N. Benard, M. Caron and E. Moreau},
booktitle={J. of Phys. Conf. Ser. 646 012055},
year={2015}
}
@inproceedings{aupoix,
title={Wall Roughness Modelling with k-omega {SST} Model},
author={Aupoix, B.},
booktitle={Proceedings of 10th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM10), Marbella, Spain, 17-19 September},
year={2014}
}
@inproceedings{nebenfuhr_2014a,
title={{INFLUENCE OF A FOREST CANOPY ON THE NEUTRAL ATMOSPHERIC BOUNDARY LAYER - A LES STUDY}},
author={Nebenf{\"u}hr, B. and Davidson, L.},
booktitle={Proceedings of 10th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM10), Marbella, Spain, 17-19 September},
year={2014}
}
The PANS and PITM model: a new formulation of $f_k$
}
%
@inproceedings{davidson:18,
title={{The PANS and PITM model: a new formulation of $f_k$}},
author={Davidson, L. and Friess, C.},
booktitle={Proceedings of 12th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM12), Montpelier,
France 26-28 September},
year={2018}
}
@inproceedings{nebenfuhr_2014b,
title={{Development of a reduced-order model for wind turbine response to atmospheric turbulence in forest regions}},
author={Nebenf{\"u}hr, B. and Carlen, I. and Caracoglia, L. and Davidson, L.},
booktitle={Proceedings of 6th International Symposium on Computational Wind Engineering, Hamburg, Germany, 8-12 June},
year={2014}
}
@inproceedings{davidson:15,
author = "L. Davidson",
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booktitle={Progress in Hybrid RANS-LES Modelling},
volume={130},
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doi={10.1007/978-3-319-15141-0_29},
title="Two non-zonal approaches to accelerate
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publisher={Springer Berlin Heidelberg},
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%url={http://dx.doi.org/10.1007/978-3-319-15141-0_29},
@incollection{sebastian:14a,
year={2014},
isbn={ISBN 978-3-319-15140-3},
booktitle={Progress in Hybrid RANS-LES Modelling},
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series={Notes on Numerical Fluid Mechanics and Multidisciplinary Design},
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title={Prediction of Transonic Duct Flow Using a Zonal Hybrid
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url={http://dx.doi.org/10.1007/978-3-319-15141-0_29},
publisher={Springer Berlin Heidelberg},
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year = 2010,
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annote = "LES" ,
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title = "Fluid flow and conjugate heat transfer in a matrix of surface-mounted cubes: A {PANS} study",
journal = ijhff,
volume=51,
pages="166--174",
year = 2015}
@article{foroutan:14,
annote = "LES" ,
author = "H. Foroutan and S. Yavuzkurt",
title = "A partially-averaged {N}avier-{S}tokes model for the simulation
of turbulent swirling flow with vortex breakdown",
journal = ijhff,
volume=50,
pages="402--416",
year = 2014}
@article{schlatter:14,
annote = "LES" ,
author = "G. Eitel-Amor and R. Orlu and P. Schlatter",
title = "Simulation and validation of a spatially evolving turbulent boundary layers up
to ${Re}_\theta = 8300$ ",
journal = ijhff,
volume=47,
pages="57--69",
year = 2014}
@misc{helgason:krajnovic:12,
author = "E. Helgason and S. Krajnovi{\'c}",
title = "Aerodynamic shape optimization of a pipe using the adjoint
method",
howpublished = "IMECE/ASME",
address ="Houston, Texas",
year = 2012}
%lee articles
@inproceedings{martin:lee:10,
title="Aero-Acoustics and Performance Modeling of a Counter-Rotating Propfan",
author = "Martin Olausson and Richard Avellan and Niklas S{\"o}rman and Filip
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booktitle = "ASME Turbo Expo",
volume=7,
pages="747--756",
address ="Glasgow, UK",
year = 2010 }
@article{tam1993dispersion,
title={Dispersion-relation-preserving finite difference schemes for computational acoustics},
author={Tam, Christopher KW and Webb, Jay C},
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volume={107},
number={2},
pages={262--281},
year={1993}
}
@article{burak:bilsson:lee:09,
title={Validation of a Time- and
Frequency-Domain Grazing Flow Acoustic Liner Model},
author="Markus O. Burak and Mattias Billson and Lars-Erik Eriksson and Stéphane Baralon",
journal="AIAA Journal",
volume={47},
number={8},
pages="1841--1848",
year={2008},
publisher={Wiley Online Library}
}
@article{billson:eriksson:davidson:04,
author = "M. Billson and L.-E. Eriksson and L. Davidson",
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journal = aiaa,
volume="43",
number =4,
pages ="752--759",
year = 2005 }
@article{burak:bilsson:lee:12,
title="Experimental and
Numerical Investigation of a Supersonic Convergent-Divergent Nozzle",
author="Markus O. Burak and Lars-Erik Eriksson and David Munday and Ephraim Gutmark
and Erik Prisell",
journal="AIAA Journal",
volume={50},
number={7},
pages="1462--1475",
year={2012},
publisher={Wiley Online Library}
}
@article{nian:lee:08,
title="Prediction of flowfield and acoustic signature of a coaxial jet using
{RANS}-based methods and large-eddy simulation",
author="N. Andersson and L.-E. Eriksson",
journal="International Journal of Aeroacoustics",
volume={7},
number={1},
pages="23--40",
year={2008},
}
@article{andersson:eriksson:davidson:05b,
author = "N. Andersson and L.-E. Eriksson and L. Davidson",
title = "Large-Eddy Simulation of Subsonic Turbulent Jets and Their Radiated Sound",
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volume = "43",
number = "9",
pages = "1899--1912",
year = 2005 }
@article{ffowcs:69,
author = "J. E. Ffowcs Williams and D. L. Hawkins",
title = "Sound Generation by Turbulence and Surfaces
in Arbitrary Motion",
journal = prsoc,
volume = "A 264 No. 1151",
pages = "321--342",
year = 1969 }
%hani articles, start
@article{nilsson2003validations,
title={Validations of CFD against detailed velocity and pressure measurements in water turbine runner flow},
author={Nilsson, H{\aa}kan and Davidson, Lars},
journal={International journal for numerical methods in fluids},
volume={41},
number={8},
pages={863--879},
year={2003},
publisher={Wiley Online Library}
}
@article{gyllenram2008design,
title={Design and Validation of a Scale-Adaptive Filtering Technique for LRN Turbulence Modeling of Unsteady
Flow},
author={Gyllenram, Walter and Nilsson, H{\aa}kan},
journal={Journal of fluids engineering},
volume={130},
number={5},
year={2008},
publisher={American Society of Mechanical Engineers}
}
@article{petit2011unsteady,
title={Unsteady Simulations of the Flow in a Swirl Generator, Using OpenFOAM},
author={Petit, Olivier and Bosioc, Alin I and Nilsson, H{\aa}kan and Muntean, Sebastian and Susan-Resiga,
Romeo F},
journal={International Journal of Fluid Machinery and Systems},
volume={4},
number={1},
pages={199--208},
year={2011}
}
@inproceedings{moradnia2011parametric,
title={A parametric study of the air flow in an electric generator through stepwise geometry modifications},
author={Moradnia, Pirooz and Nilsson, H{\aa}kan},
booktitle={An ECCOMAS Thematic Conference, CFD and OPTIMIZATION},
year={2011}
}
@inproceedings{vallier2011procedure,
title={Procedure for the break-up of cavitation sheet},
author={Vallier, Aur{\'e}lia and Revstedt, Johan and Nilsson, H{\aa}kan},
booktitle={4-th International Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems,
October, 26-28, 2011, Belgrade, Serbia},
pages={77--85},
year={2011}
}
@article{gyllenram2007failure,
title={On the failure of the quasicylindrical approximation and the connection to vortex breakdown in
turbulent swirling flow},
author={Gyllenram, Walter and Nilsson, H{\aa}kan and Davidson, Lars},
journal={Physics of Fluids},
volume={19},
number={4},
year={2007}
}
@article{nilsson2003application,
title={Application of an angular momentum balance method for investigating numerical accuracy in swirling
flow},
author={Nilsson, H{\aa}kan and Davidson, Lars},
journal={Journal of fluids engineering},
volume={125},
number={4},
pages={723--730},
year={2003},
publisher={American Society of Mechanical Engineers}
}
@article{karlsson2009numerical,
title={Numerical estimation of torsional dynamic coefficients of a hydraulic turbine},
author={Karlsson, Martin and Nilsson, H{\aa}kan and Aidanp{\"a}{\"a}, Jan-Olov},
journal={International Journal of Rotating Machinery},
year={2009},
publisher={Hindawi Publishing Corporation}
}
@inproceedings{moradnia2012experimental,
title={EXPERIMENTAL AND NUMERICAL STUDY OF COOLING AIR FLOW IN A HYDROELECTRIC GENERATOR},
author={Moradnia, Pirooz and Chernoray, Valery and Nilsson, H{\aa}kan},
booktitle={European Research Community On Flow, Turbulence and Combustion, ETMM9},
year={2012}
}
@article{nilsson2012effects,
title={Effects of inlet boundary conditions, on the computed flow in the Turbine-99 draft tube, using
OpenFOAM and CFX},
author={Nilsson, H{\aa}kan and Cervantes, Michel J},
booktitle={IOP Conf. Ser.: Earth Environ. Sci. 15 032002.},
year={2012}
}
@inproceedings{hartono2012piv,
title={PIV measurements of air flow in a hydro power generator model},
author={Hartono, Erwin A and Golubev, Maxim and Moradnia, Pirooz and Chernoray, Valery and Nilsson,
H{\aa}kan},
booktitle={16th Int Symp on Applications of Laser Techniques to Fluid Mechanics},
year={2012}
}
@inproceedings{nilsson2012simulations,
title={Simulations of the vortex in the Dellenback abrupt expansion, resembling a hydro turbine draft tube
operating at part-load},
author={Nilsson, H{\aa}kan},
booktitle={IOP Conf. Ser.: Earth Environ. Sci. 15 022016.},
year={2012}
}
%hani articles, end
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@book{brimblecombe,
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volume={117},
series={Notes on Numerical Fluid Mechanics and Multidisciplinary Design},
editor={Fu, Song and Haase, Werner and Peng, Shia-Hui and Schwamborn, Dieter},
doi="10.1007/978-3-642-31818-4\_26",
title={Hybrid RANS-LES Simulation of Turbulent High-Lift Flow in Relation to Noise Generation},
url={http://dx.doi.org/10.1007/978-3-642-31818-4\_26},
publisher={Springer Berlin Heidelberg},
author={B. Nebenf{\"u}hr and S.-H. Peng and L. Davidson},
pages={303-314}
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type = "{NTS} contribution to {ATAAC} Deliverable {D}2.2-33",
year = 2012,
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institution = "Div. of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
year = 2013,
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annote = "",
author = "B. Nebenf{\"u}hr",
title="Aerodynamic and Aeroacoustic Analysis of a Multi-Element Airfoil using Hybrid RANS/LES Modeling
Approaches",
institution = "Div. of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
year = 2012,
}
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annote = "",
author = "S. Arvidson",
title="Assessment and Some Improvements of Hybrid {RANS-LES} Methods",
institution = "Div. of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology",
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type = "Thesis for Licentiate of Engineering",
year = 2013,
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annote = "",
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type = "Thesis for Licentiate of Engineering",
year = 2012,
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annote = "",
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type = "Thesis for Licentiate of Engineering",
year = 2011,
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author = "L. Davidson",
title = "Large Eddy Simulation of Heat Transfer in Boundary layer and Backstep Flow Using {PANS}
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booktitle = "Turbulence, Heat and Mass Transfer, THMT-12",
address ="Palermo, Sicily/Italy",
year = 2012}
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author = "S.-H. Peng",
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address ="Palermo, Sicily/Italy",
year = 2012}
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author = "L. Davidson",
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booktitle = "ETMM9: 9th International ERCOFTAC Symposium on Turbulence Modelling and Measurements",
address ="Thessaloniki, Greece",
year = 2012}
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author = "I. Yilmaz and L. Davidson and O. Edis and H. Saygin",
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journal = "Journal of Physics: Conference Series",
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annote = "",
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author = "A. Bechmann and N. N. S\o rensen",
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year = "2007"}
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author = "A. Bechmann and N. N. S\o rensen",
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year = "2010"}
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author = "P. Spalart and S. Deck and M. Shur and K. Squires and M. Strelets
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journal = "Theoretical and Computational Fluid Dynamics",
publisher = "Springer Berlin/Heidelberg",
issn = "0935-4964",
keyword = "Physics and Astronomy",
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volume = 20,
issue = 3,
url = "http://dx.doi.org/10.1007/s00162-006-0015-0",
note = "10.1007/s00162-006-0015-0",
year = "2006",
}
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annote = "",
author = "F. Mathey and D. Cokljat",
title = "Zonal Multi-domain
{RANS/LES} Simulation of Air Flow over the Ahmed Body",
booktitle = "Engineering Turbulence Modelling and Measurements 6",
editor = "W. Rodi and M. Mulas",
pages ="647--656",
publisher = "Elsevier",
year = 2005
}
@inproceedings{huadong:12a,
author = "H.-D. Yao and L. Davidson and L.-E. Eriksson and O. Grundestam
and S.-H. Peng and P. E. Eliasson",
title = "Surface Integral Analogy Approaches to Computing Noise Generated by a {3D}
High-Lift Wing Configuration",
booktitle = "50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
Aerospace Exposition, AIAA paper 2012-0386",
address =" 9 -- 12 January",
year = 2012 }
@inproceedings{eliasson:12,
author = "P. E. Eliasson and O. Grundestam and S.-H. Peng and H.-D. Yao
and L. Davidson and L.-E. Eriksson",
title = "Assessment of High-lift Concepts for a Regional Aircraft in the {ALONOCO} Project",
booktitle = "50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
Aerospace Exposition, AIAA paper 2012-0277",
address =" 9 -- 12 January",
year = 2012 }
@inproceedings{grundestam:12,
author = "O. Grundestam and S.-H. Peng and P. E. Eliasson and H.-D. Yao and
L.-E. Eriksson and L. Davidson",
title = "Local flow properties in relation to noise generation for low-noise high-lift
configurations",
booktitle = "50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
Aerospace Exposition, AIAA paper 2012-0278",
address =" 9 -- 12 January",
year = 2012 }
@inproceedings{huadong:12b,
author = "H.-D. Yao and L.-E. Eriksson and L. Davidson and O. Grundestam
and S.-H. Peng and P. E. Eliasson",
title = "Aeroacoustic Assessment of Conceptual Low-Noise High-Lift Wing Configurations",
booktitle = "50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and
Aerospace Exposition, AIAA paper 2012-0383",
address =" 9 -- 12 January",
year = 2012 }
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author = "L. Davidson and S.-H. Peng",
title = "Embedded {LES} with {PANS}",
booktitle = "6th AIAA Theoretical Fluid Mechanics Conference, AIAA paper 2011-3108",
address ="27-30 June, Honolulu, Hawaii",
year = 2011 }
@inproceedings{andersson:10,
author = "B. Andersson and S. Jakobsson and A. Mark and L. Davidson and F. Edelvik",
title="Modeling Surface Tension in SPH by Interface Reconstruction using Radial Basis Functions",
booktitle = "5th international {SPHERIC} workshop",
address=" Manchester, UK",
year = 2010 }
@inproceedings{el-alit:11,
author = "M. El-ALti and V. Chernoray and M. Jahanmiri and L. Davidson",
title="Experimental and Computational Studies of Active Flow Control on a Model Truck-Trailer",
booktitle = "EFM 11: Experimental Fluid Mechanics",
volume="2",
pages="600--615",
year = 2011 }
@article{ilyas:davidson:11,
author = "I. Yilmaz and L. Davidson and O. Edis and H. Saygin",
title = "Numerical simulation of Kelvin-Helmholtz instability using an implicit, non-dissipative
{DNS} algorithm",
journal = "J. Phys.: Conf. Series",
volume="318",
number="032024",
year = 2011 }
@article{yakhot:10,
annote = "PDF",
author = "V. Yakhot and S. C. C. Bailey and A. J. Smits",
title = "Scaling of global properties of turbulence
and skin friction in pipe and channel flows",
journal = jfm,
volume =652,
pages ="65--73",
year = 2010 }
@article{schlatter:orlu:10,
annote = "PDF",
author = "P. Schlatter and R. Orlu",
title = "Assessment of direct numerical simulation data of turbulent boundary layers",
journal = jfm,
volume =659,
pages ="116--126",
year = 2010 }
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annote = "PDF",
author = "S. S. Girimaji and E. Jeong and R. Srinivasan",
title = "Partially-{A}veraged {N}avier-{S}tokes
Method for Turbulence: Fixed Point Analysis and Comparison
With Unsteady Partially Averaged {N}avier-{S}tokes",
journal = "ASME Journal of Applied Mechanics",
doi="10.1115/1.2173677",
volume =73,
number =3,
pages ="422--429",
year = 2006 }
@conference{sinisa:pans,
annote = "",
author = "B. Basara and S. Krajnovi{\'c} and S. Girimaji",
title = "{PANS} vs. {LES} for computations of the flow around a
{3D} bluff body",
booktitle = "2nd International Conference on Turbulence and Interaction",
address = "Martinique, France",
year = 2009 }
@article{terracol:06,
annote = "PDF" ,
author = "M. Terracol",
title = "A Zonal {RANS/LES} Approach for Noise Sources Prediction",
journal = ftac,
volume = 77,
number="1--4",
pages ="161--184",
year = 2006 }
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annote = "PDF" ,
author= "M. L. Shur and P. R. Spalart and M. Kh. Strelets and A. Travin",
title = "A Rapid and Accurate Switch from {RANS} to {LES} in Boundary Layers Using an Overlap Region",
journal = ftac,
number = 2,
volume = 86,
pages ="179--206",
year = 2011 }
@article{avdis:lardeau:leschziner:09,
annote = "PDF" ,
author = "A. Avdis and S. Lardeau and M. A. Leschziner",
title = "Large Eddy Simulation of Separated Flow
over a Two-dimensional Hump with and without Control by Means
of a Synthetic Slot-jet",
journal = ftac,
volume = 83,
number=3,
pages ="343--370",
year = 2009 }
@article{menter:sas:theory:10,
annote = "PDF" ,
author = "F. R. Menter and Y. Egorov",
title = "The Scale Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. {P}art 1: Theory
and Description",
journal = ftac,
volume = 85,
pages ="113--138",
year = 2010 }
@article{menter:sas:application:10,
annote = "PDF" ,
author = "Y. Egorov and F. R. Menter and R. Lechner and D. Cokljat",
title = "The Scale Adaptive Simulation Method for Unsteady Flow Predictions.
{P}art 2: Application to Complex Flows",
journal = ftac,
volume = 85,
pages ="139--165",
year = 2010 }
@misc{turb_model:lecturenotes,
annote = "" ,
author = "L. Davidson",
title = "{MTF270} {T}urbulence Modelling,
{\tt http://www.tfd.chalmers.se/\textasciitilde lada/comp\_turb\_model/},
{D}ivision of {F}luid {D}ynamics,
{D}ept. of {A}pplied {M}echanics,
{C}halmers {U}niversity of {T}echnology, {G\"o}teborg, {S}weden",
year = 2010 }
@misc{synt:10,
author = "L. Davidson",
title = "How to Implement Synthetic Inlet Boundary Conditions",
year = 2013 }
@misc{billson:aniso:04,
author = "M. Billson and L.-E. Eriksson and L. Davidson and P. Jordan",
title = "Modeling of Synthetic Anisotropic Turbulence and its Sound Emission",
booktitle = "10th AIAA/CEAS Aeroacoustics Conference, Manchester, United Kindom",
howpublished = "AIAA 2004-2857",
year = 2004 }
@misc{rumsey:04,
author = "C. Ramsey and T. B. Gatski and W. L. Seller III and V. N. Vatsa
and S. A. Viken",
title = "Summary of the 2004 {CFD} Validation Workshop on Synthetic Jets
and Turbulent Separation Control",
booktitle = "2nd AIAA Flow Control Conference, June 28-July 1, Portland, OR",
howpublished = "AIAA-2004-2217",
year = 2004 }
@misc{greenblatt:05,
author = "D. Greenblatt and K. B. Paschal and C.-S. Yao and
J. Harris",
title = "A Separation Control {CFD} Validation Test Case
{P}art 1: Zero Efflux Oscillatory Blowing",
booktitle = "43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV",
howpublished = "AIAA-2005-0485",
year = 2005 }
@misc{greenblatt:04,
author = "D. Greenblatt and K. B. Paschal and C.-S. Yao and
J. Harris and N. W. Schaeffler and A. E. Washburn",
title = "A Separation Control {CFD} Validation Test Case.
{P}art 1: Baseline \& Steady Suction",
booktitle = "2nd AIAA Flow Control Conference, Portland, OR",
howpublished = "AIAA-2004-2220",
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publisher = "Elsevier",
year = 2005}
@article{xiao:edwards:hassan:04,
annote = "LES",
author = "X. Xiao and J. R. Edwards and H. A. Hassan",
title = "Blending Dunctions in Hybrid Large-Eddy/{R}eynolds-Averaged {N}avier-{S}tokes Simulations",
journal = aiaa,
volume =42,
number =12,
pages ="2508--2515",
year = 2004 }
@misc{menter:egorov:05,
annote = "LES",
author = "F. R. Menter and Y. Egorov",
title = "A Scale-Adaptive Simulation Model Using Two-Equation Models",
howpublished = "AIAA paper 2005--1095, Reno, NV",
year = 2005 }
@article{taylor:glauser:04,
annote = "",
author = "J. A. Taylor and M. N. Glauser",
title = "Towards Practical Flow Sensing and Contorl via {POD} and {LSE} Based
on Low-Dimensional Tools",
journal = jfe,
volume =126,
pages ="337--345",
year = 2004 }
@article{younis:berger:04,
annote = "TUR",
author = "B. A. Younis and S. A Berger",
title = "A Turbulence Model for Pulsative Arterial Flows",
journal = jfe,
volume =126,
pages ="578--584",
year = 2004 }
@article{krajnovic:davidson:05a,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Flow around a Simplified Car. Part {I}: Large Eddy Simulations",
journal = jfe,
volume =127,
pages ="907--918",
number =5,
year = 2005 }
@article{krajnovic:davidson:05b,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Flow around a Simplified Car. Part {II}: Understanding the Flow",
volume =127,
number =5,
pages ="919--928",
journal = jfe,
year = 2005 }
@article{krajnovic:davidson:05c,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Influence of Floor Motions in Wind Tunnels on the Aerodynamics of Road Vehicles",
volume =92,
number =5,
pages ="677--696",
journal = jwes,
year = 2005 }
@article{walters:leylek:04,
annote = "IUR",
author = "D. K. Walters and J. H. Leylek",
title = "A New Model for Boundary Layer Transition Using Single-Point {RANS} Approach",
journal = turbo,
volume =126,
pages ="193--202",
year = 2004 }
@conference{davidson:05,
author = "L. Davidson",
title = "Hybrid {LES-RANS}: Inlet Boundary Conditions",
booktitle = "3rd National Conference on Computational Mechanics -- MekIT'05 (invited paper)",
address = "Trondheim, Norway" ,
editor ="B. Skallerud and H. I. Andersson",
pages ="7--22",
date = "May 11-12" ,
year = 2005 }
@article{kjellgren:05,
author = "P. Kjellgren",
title = "A Semi-Implicit {ALE/FE} Method for Fluid-Structure Interaction (submitted)",
journal = ijnmf,
year = 2005 }
@conference{kjellgren:barut:madenci:99,
author = "P. Kjellgren and A. Barut and E. Madenci",
title = "Finite Element Analysis for Fluid-Structure Interaction of Composite Structures",
booktitle = "Melosh Finite Element Medal Competition (Invited paper)",
address ="Duke University",
year = 1999}
@article{kjellgren:98,
author = "P. Kjellgren",
title = "An Arbitrary Lagrangian-Eulerian Finite Element Method",
journal = "Computational Mechanics",
volume =21,
pages ="81--90",
year = 1998 }
@article{kjellgren:97,
author = "P. Kjellgren",
title = "A Semi-Implicit Fractional Step Finite Element Method for Viscous Incompressible Flows",
journal = "Computational Mechanics",
volume =20,
pages ="541--550",
year = 1997 }
@conference{kjellgren:yagawa:93,
annote = "",
author = "P. Kjellgren and G. Yagawa",
title = "Large eddy simulation of turbulent flows using the finite element method",
booktitle = "Proc. 5th Int. Symposium on Computational Fluid Dynamics",
volume =3,
pages ="369--374",
address ="Sendai, Japan",
year = 1993 }
@techreport{obai:04,
annote = "" ,
author = "O. T. Younis",
title = "Formulation, Implementation and Testing of k-omega-v2-f Model in an Asymmetric Plane Diffuser",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "MSc Thesis",
number= "04/17 (can be downloaded from {\tt www.tfd.chalmers/\textasciitilde lada/msc\_thesis.html})",
year = 2004,
}
@conference{jarrin:benhamadouche:laurence:05,
annote = "LES" ,
author = "N. Jarrin and S. Benhamadouche and D. Laurence",
title = "Inlet Conditions for Large-Eddy Simulation Using a New Vortex Method",
booktitle = "The Fourth International Symp. on
Turbulence and Shear Flow Phenomena",
editor ="J. A. C. Humphrey and J. K. Eaton and
R. Friedrich and N. Kasagi and M. A. Leschziner and T. B. Gatski",
address ="Williamsburg, Virginia",
year = 2005}
@article{kotsovinos:91,
annote ="" ,
author = "N. E. Kotsovinos",
title = "Turbulence Spectra in Free Convection Flow",
journal = pha,
volume = 3,
number = 1,
pages = "163--167",
year = 1991}
@article{smirnov:shi:celik:01,
annote ="PFD-articles" ,
author = "A. Smirnov and S. Shi and I. Celik",
title = "Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling",
journal = jfe,
volume = 123,
number = 2,
pages = "359--371",
year = 2001}
@article{pallares:grau:davidson:05,
annote = "",
author = "J. Pallares and F. X. Grau and L. Davidson",
title = "Pressure Drop and Heat Transfer Rates in Forced Convection Rotating Square Duct
at High Rotation Rates",
journal =ph,
volume = 17,
number = 7,
year =2005}
@article{tian:00a,
annote = "PDF-file",
author = "Y. Tian and T. G. Karayiannis",
title = "Low turbulence natural convection in an air cavity filled square cavity -- Part I:
the thermal and fluid flow fields",
journal = ihmt,
volume="43",
number = "6",
pages="849--866",
year = 2000 }
@article{tian:00b,
annote = "PDF-file",
author = "Y. Tian and T. G. Karayiannis",
title = "Low turbulence natural convection in an air cavity filled square cavity --
Part II: the turbulence quantities ",
journal = ihmt,
volume="43",
number = "6",
pages="867--884",
year = 2000 }
@article{hamba:03a,
annote = "PDF-file",
author = "F. Hamba",
title = "A Hybrid {RANS/LES} Simulation of Turbulent Channel Flow",
journal = theor,
volume="16",
pages ="387--403",
year = 2003 }
@article{salat:xin:joubert:sergent:penot:quere:04,
annote = "LES",
author = "J. Salat and S. Xin and P. Joubert and A. Sergent and F. Penot and P. Le Qu{\'e}r{\'e}",
title = "Experimental and Numerical Investigation of Turbulent Natural Convection in a Large
Air-Filled Cavity",
journal = ijhff,
volume ="25",
pages ="824--832",
year = 2004 }
@article{davidson:billson:05,
annote = "",
author = "L. Davidson and M. Billson",
title = "Hybrid {LES/RANS} Using Synthesized Turbulent fluctuations for Forcing in the Interface region",
journal = ijhff,
volume ="27",
number =6,
pages ="1028--1042",
year = 2006 }
@conference{peng:davidson:hanjalic:05,
author = "S.-H. Peng and L. Davidson and K. Hanjali{\'c}",
title = "Numerical Analysis of {R}ayleigh-{B}{\'e}nard Convection Flow Using Large Eddy Simulation
at high {R}ayley Numbers",
booktitle = "The Fourth International Symp. on
Turbulence and Shear Flow Phenomena",
editor ="J. A. C. Humphrey and J. K. Eaton and
R. Friedrich and N. Kasagi and M. A. Leschziner and T. B. Gatski",
address ="Williamsburg, Virginia",
year = 2005}
@conference{darioush:davidson:rolf:05,
annote = "",
author = "D. G. Barhaghi and L. Davidson and R. Karlsson",
title = "Large Eddy Simulation of Natural Convection Boundary Layer on a Vertical Cylinder",
booktitle = "Engineering Turbulence Modelling and Measurements -- {ETMM6}",
editor = "W. Rodi and M. Mulas",
pages ="287--296",
publisher = "Elsevier",
year =2005,
}
@techreport{davidson:desider:05,
annote = "" ,
author = "L. Davidson",
title = "Definition of test case 09: channel flow. Version 1.",
institution = "Division of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "DESider report",
year = 2005,
}
@misc{byun:simpson:05,
annote = "Exp",
author = "G. Byun and R. L. Simpson",
title = "Structure of Three-Dimensional Seprated Flow on an Axisymmetric Bump",
howpublished = "AIAA paper 2005-0113, Reno, N.V.",
year = 2005 }
@article{sveningsson:davidson:05,
author = "A. Sveningsson and L. Davidson",
title = "Computations of Flow Field and Heat Transfer in a Stator Vane
Passage using the $\overline{v^2}-f$ Turbulence Model",
journal = "Journal of Turbomachinery",
volume =127,
number =3,
pages = "627--634",
year = 2005 }
@@conference{sveningsson:pettersson:reif:davidson:05,
author = "A. Sveningsson and B. A. {Pettersson-Reif} and L. Davidson",
title = "Modelling the Entrance Region in a Plane Asymmetric Diffuser by
Elliptic Relaxation",
booktitle = "The Fourth International Symp. on
Turbulence and Shear Flow Phenomena",
editor ="J. A. C. Humphrey and J. K. Eaton and
R. Friedrich and N. Kasagi and M. A. Leschziner and T. B. Gatski",
address ="Williamsburg, Virginia",
year = 2005}
@article{andersson:eriksson:davidson:05a,
author = "N. Andersson and L.-E. Eriksson and L. Davidson",
title = "Investigation of an Isothermal {M}ach 0.75 Jet and its Radiated sound Using Large-Eddy
Simulation and {K}irchhoff Surface Integration",
journal = ijhff,
volume =26,
number =3,
pages="393--410",
year = 2005 }
@misc{andersson:eriksson:davidson:05c,
author = "N. Andersson and L.-E. Eriksson and L. Davidson",
title ="{LES} Prediction of Flow an Acoustic Field of a Coaxial Jet",
howpublished = "11th AIAA/CEAS Aeroacoustics Conference, AIAA 2005-2884, May 23-25, Monterey, California",
year = 2005 }
@misc{andersson:eriksson:davidson:05d,
author = "N. Andersson and L.-E. Eriksson and L. Davidson",
title ="Effects of Inflow Conditions and Subgrid Model on {LES} for Turbulent Jets",
howpublished = "11th AIAA/CEAS Aeroacoustics Conference, AIAA 2005-2925, May 23-25, Monterey, California",
year = 2005 }
@article{bryce:lien:davidson:cn:04,
author = "B. Sharman and F. S. Lien and L. Davidson and C. Norberg",
title = "Numerical Prediction of low {R}eynolds Number Flows Over Two Tandem Circular Cylinders",
journal = ijnmf,
volume="47",
pages ="423--447",
year = 2005 }
@techreport{aldo:04,
annote = "" ,
author = "A. G. B Mor\'{a}n",
title = "Prediction of the Axisymmetric Impinging Jet with Different $k-\varepsilon$ Turbulence Models",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "MSc Thesis",
number= "04/29 (can be downloaded from {\tt www.tfd.chalmers/\textasciitilde lada/msc\_thesis.html})",
year = 2004,
}
@techreport{vagesh:04,
annote = "" ,
author = "V. D. Narasimhamurthy",
title = "Unsteady-{RANS} Simulation of Turbulent Trailing-Edge Flow",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "MSc Thesis",
number= "04/31 (can be downloaded from {\tt www.tfd.chalmers/\textasciitilde lada/msc\_thesis.html})",
year = 2004,
}
@techreport{wollblad:lic,
annote = "",
author = "C. Wollblad",
title = "Large Eddy Simulation of Transonic Flow with Shock Wave/Turbulent Boundary Layer Interaction",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "04/07",
year = 2004,
}
@techreport{darioush:lic,
annote = "",
author = "D. G. Barhaghi",
title = "{DNS} and {LES} of Turbulent Natural Convection Boundary Layer",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "04/06",
year = 2004,
}
@book{welty:wicks:wilson:84,
annote = "",
author = "J. R. Welty and C. E. Wicks and R. E. Wilson",
title = "Fundamentals of Momentum, Heat, and Mass Transfer",
publisher = "John Wiley \& Sons",
edition =3,
address = "New York",
year = 1984 }
@article{lardeau:leschziner:li:04,
annote = "TUR",
author = "S. Lardeau and M. A. Leschziner and N. Li",
title = "Modelling Bypass Transition with Low-Reynolds-Number Nonlinear Eddy-Viscosity Closure",
journal = ftac,
volume="73",
pages ="49--76",
year = 2004 }
@book{flomania:book,
annote = "",
editor = "W. Haase and B. Aupoix and U. Bunge and D. Schwamborn",
title = "{FLOMANIA}: Flow-Physics Modelling -- An Integrated Approach",
series = "Notes on Numerical Fluid Mechanics and Multidisciplinary Design",
volume="94",
publisher = "Springer",
year = 2006 }
@article{pierce:moin:98,
annote = "LES",
author = "C. D. Pierce and P. Moin",
title = "Method for Generating Equilibrium Swirling Inflow Conditions",
journal = aiaa,
volume="36",
number =7,
pages ="1325--1327",
year = 1998 }
@inproceedings{esch:menter:03,
annote = "TUR",
author = "T. Esch and F. R. Menter",
title = "Heat Transfer Predictions Based on Two-Equation Turbulence
Models with Advanced Wall Treatment",
booktitle = "Turbulence Heat and Mass Transfer 4",
editor = "K. Hanjali{\'c} and Y. Nagano and M. J. Tummers",
publisher = "begell house, inc.",
pages = "633--640",
address = "New York, Wallingford (UK)",
year = 2003 }
@article{craft:gerasimov:iacovides:launder:02,
annote = "PDF-files",
author = "T. J. Craft and A. V. Gerasimov and H. Iacovides and B. E. Launder",
title = "Progress in the Generalization of Wall-Function Treatments",
journal = ijhff,
volume = 23,
number =2,
pages = "148--160",
year = 2002 }
@incollection{krajnovic:davidson:04a,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Exploring the Flow Around a Simplified Bus with Large Eddy Simulation and Topological Tools",
editor = "Rose McCallen and Fred Browand and James Ross",
booktitle = "The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains",
series = "Lecture Notes in Applied and Computational Mechanics",
volume =19,
publisher = "Springer Verlag",
year = 2004 }
@article{ask:davidson:05,
annote = "",
author = "J. Ask and L. Davidson",
title = "An acoustic analogy applied to incompressible flow fields",
journal = "Comptes Rendus Mecanique",
volume = 333,
number =9,
pages = "657--732",
year = 2005 }
@misc{shur:strelets:travin:03a,
annote = "LES",
author = "M. Shur and M. Strelets and A. Travin",
title = "Detached Eddy Simulation ({DES}):
General Description, Existing Versions, Constants Calibration, and Overview of Applications",
howpublished = "Deliverable D4.4-15, Flomania project {\tt http://cfd.me.umist.ac.uk/flomania/}",
year = 2003}
@article{gullman:tornblom:lindgren:amberg:johansson:04,
annote = "PDF",
author = "J. Gullman-Strand and Ol. t{\"o}rnblom and B. Lindgren and G. Amberg and A. V. Johansson",
title = "Numerical and Experimental Study of Separated Flow in a Plane Asymmetric Diffuser",
journal = ijhff,
volume ="25",
pages = "451--460",
year = 2004 }
@article{george:davidson:04,
annote = "",
author = "W. K. George and L. Davidson",
title = "Role of Initial Conditions in Establishing Asymptotic Flow Behavior",
journal = aiaa,
volume="42",
number =3,
pages ="438--446",
year = 2004 }
@article{byun:simpson:long:04,
annote = "Exp",
author = "G. Byun and R. L. Simpson and C. H. Long",
title = "A Study of Vortical Separation from Three-Dimensional Symmetric Bumps",
journal = aiaa,
volume="42",
number =4,
pages ="754--765",
year = 2004 }
@article{schluter:pitsch:moin:04,
annote = "LES",
author = "J.U. Schl{\"u}ter and H. Pitsch and P. Moin",
title = "Large Eddy Simulation Inflow Conditions for Coupling with
{R}eynolds-Averaged Flow Solvers",
journal = aiaa,
volume ="42",
number ="3",
pages = "478--484",
year = 2004 }
@article{batten:goldberg:chakravarthy:04,
annote = "LES",
author = "P. Batten and U. Goldberg and S. Chakravarthy",
title = "Interfacing Statistical Turbulence Closures with Large-Eddy Simulation",
journal = aiaa,
volume ="42",
number ="3",
pages = "485--492",
year = 2004 }
@article{paik:ge:sotiropoulos:04,
annote = "LES",
author = "J. Paik and L. Ge and F. Sotiropoulos",
title = "Toward the Simulation of Complex {3D} Shear Flows Using Unstead Statistical
Turbulence Models",
journal = ijhff,
volume ="25",
pages = "513--527",
year = 2004 }
@article{wang:li:jackson:04,
annote = "",
author = "J. Wang and J. Li and J. D. Jackson",
title = "A Study of the Influence Buoyancy on Turbulent Flow in a Vertical Plane Passage",
journal = ijhff,
volume ="25",
pages = "420--430",
year = 2004 }
@article{larsson:04,
author = "J. Larsson and L. Davidson and M. Olsson and L.-E. Eriksson",
title = "Aero Acoustic Investigation of an Open Cavity at Low {M}ach Number",
journal = aiaa,
volume ="42",
number ="12",
pages ="2462--2473",
year = 2004 }
@misc{menter:04a,
annote = "PDF-file",
author = "F. R. Menter and R. B. Langtry and S. R. Likki and Y. B. Suzen and P. G. Huang",
title = "A Correlation-Based Transition Model Using Local Variables. Part i -- Model Formulation",
howpublished = "Paper GT2004-53452, ASME TURBO EXPO 2004, Vienna",
address ="",
year = 2004}
@misc{menter:04a,
annote = "PDF-file",
author = "F. R. Menter and R. B. Langtry and S. R. Likki and Y. B. Suzen and P. G. Huang",
title = "A Correlation-Based Transition Model Using Local Variables. Part i -- Test Casea and Industrial
Applications",
howpublished = "Paper GT2004-53454, ASME TURBO EXPO 2004, Vienna",
address ="",
year = 2004}
@conference{wang:jang:leschziner:03,
annote = "PDF-file",
author = "C. Wang and Y. J. Jang and M. A. Leschziner",
title = "Modelling of {2D} and {3D} Separation from Curved Surfaces with Anisotropic-Resolving
Turbulence Closures",
booktitle = "The 3rd International Symp. on
Turbulence and Shear Flow Phenomena",
editor ="N. Kasagi and J. K. Eaton and R. Friedrich and J. A. C. Humphrey and
M. A. Leschziner and T. Miyauchi",
volume =1,
pages ="257--262",
address ="Sendai, Japan",
year = 2003 }
@conference{temmerman:wang:leschziner:04,
annote = "PDF-file",
author = "L. Temmerman and C. Wang and M. A. Leschziner",
title = "A Comparative Study of Separation from a Three-Dimensional Hill Using Large Eddy Simulation
and Second-Moment-Closures {RANS} Modelling",
booktitle = "ECCOMAS 2004",
address = "July 24-28, Finland",
year = 2004 }
@conference{krajnovic:davidson:02d,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Exploring the Flow Around a Simplified Bus with Large Eddy Simulation and Topological Tools",
booktitle = "The Aerodynamics of Heavy Vehicles: Trucks, Buses and Trains",
address ="Monterey-Pacific Grove, California, USA",
year = 2002 }
@incollection{travin:shur:strelets:03,
annote = "LES",
author = "A. K. Travin and M. Shur and and M. Strelets and P. R. Spalart",
title = "Physical and Numerical Upgrades in the Detached-Eddy Simulations of Complex Turbulent Flows",
booktitle = "Fluid Mechanics and its Applications. Advances in LES of Complex Flows",
editor ="R. Friederich and W.Rodi",
series = "Euromech Colloquium 412. Fluid Mechanics and its Applications. Advances in LES of Complex Flows",
volume =65,
pages ="239--254",
publisher ="Academic Publishers, Dordrecht",
year = 2002 }
@conference{hanjalic:hadziabdic:03,
annote = "LES",
author = "K. Hanjalic and M. Hadziabdic",
title = "Merging {LES} and {RANS} Strategies: Zonal or Seamless Coupling?",
year = 2003 }
@article{hanjalic:popovac:habziabdic:04,
annote = "TUR",
author = "K. Hanjalic and M. Popovacx and M. Habziabdic",
title = "A Robust Near-Wall Elliptic Relaxation Eddy-Viscosity Turbulence Model for {CFD}",
journal = ijhff,
year = 2004 }
@techreport{hoffman:johnson:03,
annote = "LES",
author = "J. Hoffman and C. Johnson",
title = "Adaptive {DNS/LES}: a New Agenda in {CFD}",
institution = "Chalmers Finite Element Center",
address ="G{\"o}teborg, Sweden",
number = "2003-23",
type = "Report",
year = 2003,
}
@techreport{hoffman:03,
annote = "LES",
author = "J. Hoffman",
title = "Adaptive Finite Element Methods for {LES}: Compuation of the Mean Drag Coefficient in a Turbulent
Flow Around a Surface Mounted Cube Using Adaptive Mesh Refinement",
institution = "Chalmers Finite Element Center",
address ="G{\"o}teborg, Sweden",
number = "2003-22",
type = "Report",
year = 2003,
}
@techreport{hellsten:03,
annote = "TUR",
author = "A. Hellsten",
title = "Behavior of Linear and Nonlinear Two-Equartoin Turbulence Models Near Interfaces of
Turbulent and Laminar Flow",
institution = "Laboratry of Aerodynamics, Helsinki University of Technology",
address ="Helsinki, Finland",
type = "Report",
year = 2003,
}
@misc{sveningsson:davidson:04b,
author = "A. Sveningsson and L. Davidson",
title = "Computations of Flow Field and Heat Transfer in a Stator Vane
Passage using the $\overline{v^2}-f$ Turbulence Model",
howpublished = "Paper GT2004-53586, ASME TURBO EXPO 2004, Vienna",
address ="",
year = 2004}
@article{pettersson:reif:durbin:ooi:99,
annote = "TUR",
author = "B. A. {Pettersson-Reif} and P. A. Durbin and A. Ooi",
title = "Modeling Rotationsl Effects in Eddy-Viscosity Closures",
journal = ijhff,
volume ="20",
pages = "563--573",
year = 1999 }
@article{sveningsson:davidson:04a,
annote = "",
author = "A. Sveningsson and L. Davidson",
title = "Assessment of Realizability Constraints in $\overline{v^2}-f$ Turbulence Models",
journal = ijhff,
volume ="25",
number ="5",
pages = "785--794",
year = 2004 }
@techreport{santhosh:03,
annote = "" ,
author = "S. T. Jayaraju",
title = "Formulation and Implementation of a $\overline{v\theta}-g$ Model to Improve the Wall Normal Turbulent
Heat Flux Predictions in a Fully Developed Channel Flow",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "MSc Thesis",
number= "03/28 (can be downloaded from {\tt www.tfd.chalmers/\textasciitilde lada/msc\_thesis.html})",
year = 2003,
}
@techreport{DES:STARCD,
annote = "LES under S",
author = "N. Andersson",
title = "STAR-CD DES",
}
@misc{wollblad:eriksson:davidson:04,
annote = "LES",
author = "C. Wollblad and L.-E. Eriksson and L. Davidson",
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year = 2004 }
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author = "N. Andersson",
title = "A Study of Subsonic Turbulent Jets and Their Radiated Sound Using Large-Eddy Simulation",
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school = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
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howpublished = "The 10th AIAA/CEAS Aeroacoustics Conference, AIAA 2004-3024, Manchester, United Kindom",
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author = "S. T. Johansen and J. Wu and W. Shyy",
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editor = "K. Hanjali{\'c} and Y. Nagano and M. J. Tummers",
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annote = "LES, PDF-files",
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title = "Hybrid {Miles}-{RANS} Method for more Dissipative Solvers and thge use of Non-Linear {LES}",
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annote = "PDF-file",
author = "G. {Lo Iacono} and P. G. Tucker",
title = "{LES} Computation of Particle Transport in Rib Roughened Passages",
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editor = "W. Rodi and N. Fueyo",
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publisher = "Elsevier",
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volume = 24,
pages = "538--550",
year = 2003}
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annote = "LES",
author = "X. Xiao and J. R. Edwards and H. A. Hassan",
title = "Inflow Boundary Conditions for {LES}/{RANS} Simulations with Applications
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year = 2003 }
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author = "L. Davidson and M. Billson",
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annote = "",
author = "L. Davidson and S. Dahlstr{\"o}m",
title = "Hybrid {LES-RANS}: An Approach to make {LES} Applicable at High {R}eynolds Number (Keynote Lecture)",
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address = "April 19-24, Norway",
year = 2004 }
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annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Large Eddy Simulation of the Flow Around an {A}hmed Body",
booktitle = "2004 ASME Heat Transfer/Fluids Engineering Summer Conference ",
address ="Charlotte, USA",
year = 2004}
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author = "N. Andersson",
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year = 2003,
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year = 2003}
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annote = "",
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booktitle = "21th IAHR Symposium",
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year = 2002 }
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number = 8,
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year = 2003}
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annote ="" ,
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volume = 125,
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year = 2003}
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year = 2004}
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author = "A. D. Apsley and M. A. Leschziner",
title = "A New Low-{R}e Non-Linear Two-Equation Turbulence Model for Complex Flows",
volume = 19,
number = 3,
journal = ijhff,
pages = "209--222",
year = 1998 }
@conference{krajnovic:davidson:00d,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Large-Eddy Simulation of the Flow Around a Ground Vehicle Body",
booktitle = "SAE Paper 2001-01-0702, Detroit",
year = 2001 }
@techreport{VEHE1,
annote = "",
author = "A. Sohankar and L. Davidson",
title = "Heat Transfer Enhancement in a Tube-Fin Heat Exchanger With Delta
Winglet Pair Vortex Generator",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
type = "{VEHE} report",
year = 1999 }
@techreport{VEHE2,
annote = "",
author = "A. Sohankar and L. Davidson",
title = "Numerical Simulation of Heat Transfer Enhancement in
Triangular Channel with Punched Delta Winglets",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
type = "{VEHE} report",
year = 1999 }
@techreport{VEHE3,
annote = "",
author = "A. Sohankar and L. Davidson",
title = "Numerical Simulation of
Heat Transfer Enhancement in Three-Dimensional Plate-Fin Heat Exchanger With
Rectangular Shape Vortex Generators",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
type = "{VEHE} report",
year = 1999 }
@article{fadlun:verzicco:orlandi:mohd-yusof:00,
annote ="LES" ,
author = "E. A. Fadlun and R. Verzicco and P. Orlandi and J. Mohd-Yusof",
title = "Combined Immersed-Boundary Finite-Difference Methods for
Three-Dimensional Complex Flow Simulations",
journal = jcphys,
volume = 161,
pages = "35--60",
year = 2000}
@article{song:degraaff:eaton:00,
annote = "EXP",
author = "S. Song and D. B. DeGraaff and J. K. Eaton",
title = "Experimental Study of a Separating, Reattaching, and Redeveloping Flow
Over a Smoothly Contoured Ramp",
journal = ijhff,
volume = 21,
number = 5,
pages = "512--519",
year = 2000 }
@article{garg:ferziger:monismith:koseff:00,
annote = "LES",
author = "R. P. Garg and J. H. Ferziger and S. G. Monismith and J. R. Koseff",
title = "Stably Stratified Turbulent Channels Flows. {I}. {S}tratification
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number = 10,
pages = "2569--2594",
year = 2000 }
@misc{dahlstrom:davidson:00,
annote = "",
author = "S. Dahlstr{\"o}m and L. Davidson",
title = "Large Eddy Simulation of the Flow Around an Airfoil",
howpublished = "AIAA paper 2001--0425, Reno, NV",
year = 2001,
}
@misc{krajnovic:davidson:00c,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Large Eddy Simulation of the Flow Around a Three-Dimensional Bluff Body",
howpublished = "AIAA paper 2001--0432, Reno, NV",
year = 2001,
}
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annote = "ACO",
author = "C. Bailly and C. Bogey and D. Juv{\'e}",
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howpublished = "AIAA paper 2000-2047",
year = 2000,
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@misc{bogey:bailly:juve:00,
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title = "Computatinal of the Sound Raidated by a 3-{D} Jet Using Large Eddy Simulation",
howpublished = "AIAA paper 2000-2009",
year = 2000,
}
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annote = "LES",
author = "P. R. Spalart",
title = "Strategies for Turbulence Modelling and Simulations",
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volume = 21,
pages ="252--263",
year = 2000 }
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annote ="LES" ,
author = "T. S. Lund and X. Wu and K. D. Squires",
title = "Generation of Turbulent Inflow Data for Spatially-Developing Boundary
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volume = 140,
pages = "233--258",
year = 1998}
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annote ="ACO" ,
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volume = 81,
pages = "403--419",
year = 1999}
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annote = "LES",
author = "N. A. Adams",
title = "Deconvolution Methods for Large-Eddy Simulation",
booktitle = "{ECCOMAS 2000}, European Congress on Computational Methods in
Applied Sciences and Engineering, 11-14 September",
address ="Barcelona, Spain",
year = 2000 }
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key="Ercoftac",
author = "{ERCOFTAC Database}",
title = "Classic Collection, http://vortex.mech.surrey.ac.uk/",
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annote = "LES",
author = "C. P. Mellen and J. Fr{\"o}hlich and W. Rodi",
title = "Large Eddy Simulation of the flow over periodic hills",
booktitle = "16th IMACS World Congress 2000, Lausanne, August 21-25",
year = 2000 }
@article{murata:mochizuku:00,
annote ="" ,
author = "A. Murata and S. Mochizuku",
title = "Large Eddy Simulation With a Dynamic Subgrid-Scale Model of Turbulent
Heat Transfer in an Orthogonally Rotating Rectangular Duct With Transverse Rib Turbulators",
journal = ihmts,
volume = 43,
pages = "1243--1259",
year = 2000}
@techreport{LESFOIL:min24:2000,
annote = "",
author = "",
title = "{LESFOIL} : Minutes of 24-months meeting,
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institution = "" }
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annote = "",
author = "P. Spalart and S. Allmaras",
title = "A One Equation Turbulence Model for Aerodynamic Flows",
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year = 1992 }
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author = "",
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annote = "",
author = "",
title = "{LES} of Flow Around {A}-Airfoil Part {II} - 3{D}
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institution = "{FLUENT}",
year = 2000 }
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annote = "",
author = "H. Nilsson and L. Davidson",
title = "A Numerical Comparison of Four Operating Conditions in a {K}aplan
Water Turbine, Focusing on Tip Clearance Flow",
booktitle = "20th IAHR Symposium",
year = 2000 }
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annote = "",
author = "S. Johansson",
title = "Numerical Simulation of Vortex Shedding Past Triangular Cylinders",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "91/7",
year = 1991}
@techreport{jansson:lic,
annote = "",
author = "S. Jansson",
title = "Numerical Investigation of Steady and Unsteady Flows Comparing
Turbulence Models and Different Near-Wall Models",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "92/1",
year = 1992}
@techreport{shankar:lic,
annote = "",
author = "V. Shankar",
title = "Numerical Investigation of Turbulent Plumes in both Ambient and
Stratified Surroundings",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "93/1",
year = 1993}
@techreport{zhou:lic,
annote = "",
author = "G. Zhou",
title = "Numerical Simulation of Transonic Flows With Special Emphasis on
Development of Pressure-Based Methods for Aerodynamic Flows",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "93/4",
year = 1993,
}
@techreport{peter:lic,
annote = "",
author = "P. Johansson",
title = "Numerical Simulations of Three-Dimensional Ventilated Enclosures
Using a Full Multigrid Method",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "94/5",
year = 1994,
}
@phdthesis{zhou:phd,
annote = "" ,
author = "G. Zhou",
title = "Numerical Simulations of Physical Discontinuities in Single and
Multi-fluid Flows for Arbitrary {M}ach Numbers",
school = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address="G{\"o}teborg, Sweden",
year = 1995 }
@techreport{hani:lic,
annote = "",
author = "H. Nilsson",
title = "A Numerical Investigation of the Turbulent Flow in a {K}aplan Water Turbine Runner",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "99/5",
year = 1999,
}
@article{zhou:davidson:95,
annote ="" ,
author = "G. Zhou and L. Davidson",
title = "A Pressure Based {E}uler Scheme for Transonic Internal and
External Flow Simulation",
journal = "Int. J. Comp. Fluid Dynamics",
volume = 5,
pages = "169--188",
year = 1995}
@article{zhou:davidson:olsson:95a,
annote ="" ,
author = "G. Zhou and L. Davidson and E. Olsson",
title = "Turbulent Transonic Airfoil Flow Simulation Using
a Pressure Based Algorithm",
journal = aiaa,
volume = 33,
pages = "42--47",
year = 1995}
@article{farhanieh:davidson:sunden:93,
annote ="" ,
author = "B. Farhanieh and L. Davidson and B. Sund{\'e}n",
title = "Second Moment Closure for Calculation of Turbulent Recirculating
Flows in Complex Geometries with Collocated Variable Arrangement",
journal = ijnmf,
volume = 16,
pages = "525--544",
year = 1993}
@INPROCEEDINGS{davidson:hedberg:olsson:89,
annote = "",
author = "L. Davidson and P. Hedberg and E. Olsson",
title = "A Finite-Volume Computer Program for Turbulent Flow in Complex Geometries",
booktitle = "Proc. 7th International Conference on Finite Element Methods in
Fluid Problems",
adress = "Huntsville, Alabama",
pages ="390--396",
year = 1989}
@INPROCEEDINGS{davidson:91,
annote = "",
author = "L. Davidson",
title = "Calculation of the Flow Around a High-Lift Airfoil Using an Explicit Code
and an Algebraic {R}eynolds Stress Model",
booktitle = " Proc. 7th Int. Conf. on Numerical Methods in Laminar and Turbulent Flow",
adress = "Stanford",
pages = "852--862",
year = 1991}
@misc{davidson:rizzi:92a,
annote = "",
author = "L. Davidson and A. Rizzi",
title = "{N}avier-{S}tokes Computation of Airfoil in Stall Using Algebraic
{R}eynolds-Stress Model",
howpublished = "AIAA-paper 92-0195, 29th Aerospace Sciences Meeting, Reno",
year = 1992}
@conference{nisbet:davidson:olsson:92,
annote = "",
author = "J. Nisbet and L. Davidson and E. Olsson",
title = "Analysis of Two Fast-Chemistry Combustion Models and Turbulence Modeling
in Variable Density Flow",
booktitle = " Proc 1st European Comp. Fluid Dynamics {'92}",
volume = 1,
pages = "557--563",
year = 1992 }
@conference{zhou:davidson:92,
annote = "",
author = "G. Zhou and L. Davidson",
title = "Transonic Flow Computations Using a Modified {SIMPLE} Code
Based on a Collocated Grid Arrangement",
booktitle = " Proc 1st European Comp. Fluid Dynamics {'92}",
volume = 2,
pages = " 749--756",
year = 1992 }
@conference{davidson:95,
annote = "",
author = "L. Davidson",
booktitle = "5th International Symposium on Refined Flow Modelling and
Turbulence Measurements",
title = "High-Lift Airfoil Flow Simulations Using a Two-Layer {R}eynolds
Stress Transport Model",
address ="Paris",
pages = "777--784",
year = 1995}
@conference{zhou:davidson:olsson:95,
annote = "" ,
author = "G. Zhou and L. Davidson and E. Olsson",
title = "Transonic Inviscid/Turbulent Airflow Flow Simulations Using a Pressure
Based Method with Higher Order Schemes",
booktitle = "Lecture Notes in Physics",
volume = "453",
publisher = "Springer",
editor ="S. M. Deshpande and S. S. Desai and R. Narasimha",
pages = "372--377",
year = 1995 }
@misc{davidson:stolcis:95,
annote = "",
author = "L. Davidson and L. Stolcis",
title = "An Efficient and Stable Solution Procedure of Compressible Turbulent Flow on
General Unstructured Meshes Using Transport Turbulence Models",
howpublished = "AIAA paper 95-0342, 33rd Aerospace Sciences Meeting, Reno",
year = 1995,
}
@INPROCEEDINGS{rokni:sunden:davidson:95,
annote = "",
author = "M. Rokni and B. Sund{\'e}n and L. Davidson",
title = "A Numerical Study of Turbulent Forced
Convection in a Square Duct Using Different Turbulence Models",
booktitle = "Numerical Methods in Thermal Problems",
address = "Atlanta",
volume = 9,
year = 1995,
pages = "205--216" }
@misc{bredberg:davidson:98,
key = "",
author = "J. Bredberg and L. Davidson",
title = "7th {ERCOFTAC/IAHR/COST} Workshop on Refined Flow Modelling.
Case 7.2: Two-Dimensional Flow and Heat Transfer over a Smooth
Wall Roughened with Squared Sectioned Rib",
address = "UMIST, Manchester",
year = 1998 }
@inproceedings{davidson:fontaine:89,
annote = "",
author = "L. Davidson and J. R. Fontaine",
title = "Calculation of the Flow in Ventilated Rooms Using Different
Finite-Difference Schemes and Different Treatment of the Walls",
booktitle = "CLIMA 2000",
address = "Sarajevo",
pages = "219--225",
year = 1989 }
@conference{perzon:davidson:00,
annote = "",
author = "S. Perzon and L. Davidson",
title = "On Transient Modeling of the Flow Around Vehicles Using the {R}eynolds
Equation",
booktitle = "ACFD 2000",
editor = "J.-H. Wu and Z.-J. Zhu and F.-P. Jia and X.-B. Wen and W. Hu",
address = "Bejing",
year = 2000 }
@conference{krajnovic:davidson:00a,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "Flow Around a Three-Dimensional Bluff Body",
booktitle = "9th International Symposium on Flow Visualisation",
address ="Heriot-Watt University, Edinburgh",
editor = "G. M. Carlomagno and I. Grant",
year = 2000 }
@conference{krajnovic:davidson:00b,
annote = "",
author = "S. Krajnovi{\'c} and L. Davidson",
title = "A New Mixed One-Equation Subgrid Model",
booktitle = "Euromech Colloquium 412: {LES} of Complex Transitional and Turbulent Flows",
address ="Munich, Germany, October 5-6",
year = 2000 }
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annote = "ACO",
author = "C. Bailly and D. Juv{\'e}",
title = "A Stochastic Approach to Compute Subsonic Noise Using Numerical Solution of
Acoustic Propagation Problems Using Linearized {E}uler Equations",
howpublished = "AIAA paper 99-1872",
year = 1999,
}
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annote = "ACO",
author = "W. B{\'e}chara and C. Bailly and P. Lafon",
title = "Stochastic Approach to Noise Modelling for Free
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journal = aiaa,
volume = 32,
number = 3,
pages = "455--463",
year = 1994}
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volume = 38,
number = 1,
pages = "22--29",
year = 2000}
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annote = "LES" ,
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number = "4",
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year = 2000 }
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year = 2000 }
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author = "S. Dahlstr{\"o}m",
title = "Large Eddy Simulation of the Flow Around a High-Lift Airfoil",
institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
number = "00/5",
month = "May",
year = 2000,
}
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year = 1998 }
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annote = "EXP",
author = "C. A. Long and A. Alexiou and N. J. Hills and A. B. Turner and J. A. Millward",
title = "Heat Transfer in a Rotating Disc-Cone Cavity With Axial Throughflow",
booktitle = "International Symposium on Transport Phenomena and Dynamics of Rotating
Machinery ({ISROMAC} - 8)",
address = "Honolulu, Hawaii",
year = 2000}
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author = "J. Bredberg and S-H. Peng and L. Davidson",
title = "On the Wall Boundary Condition for Computing Heat
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howpublished = "IMECE/ASME HTD-Vol. 365-5",
pages ="243--250",
year = 2000}
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annote = "",
author = "J. Bredberg and S-H. Peng and L. Davidson",
title = "private communication",
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year = 2000 }
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annote = "TUR",
author = "P. Rautaheimo and T. Siikonen",
title = "Improved Solid-Wall Boundary Treatment in Low-{R}eynolds Number Turbulence Models",
howpublished = "AIAA paper 2000-0136, Reno, NV",
year = 2000,
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institution = "ERCOFTAC Bullentin",
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annote = "",
author = "F. T. M. Nieuwstadt and B. A. van Haarlem",
title = "Numerical Simulation of Atmospheric Turbulence",
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pages = "190--204",
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annote = "",
author = "S-H Peng and L. Davidson",
title = "Large Eddy Simulation for Turbulent Buoyant Flows Induced
by Differentially Heated Vertical Walls",
institution = "Dept. of Thermo and Fluid Dynamics,
Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Report",
number = "98/8",
year = 1998}
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annote = "",
author = "S. Dahlstr{\"o}m and L. Davidson",
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annote = "",
author = "S.-H Peng and L. Davidson",
title = "Chalmers' 24-Month Report, Task 2, {LESFOIL} : A {B}rite-{E}uram Project",
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annote = "",
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annote = "",
author = "C. Mellen and J. Fr{\"o}hlich and W. Rodi",
title = "Karlruhe's contribution to the Final Report, {LESFOIL}: A {B}rite-{E}uram Project",
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annote = "",
author = "C. Mellen and J. Fr{\"o}hlich and W. Rodi",
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annote = "",
author = "L. Davidson",
title = "{LES-RANS} of Channel Flow",
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type = "Report",
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year = 2000 }
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annote = "LES",
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institution = "Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology",
address ="G{\"o}teborg, Sweden",
type = "Thesis for Licentiate of Engineering",
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year = 2000,
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annote = "TUR",
author = "A. Hellsten",
title = "On the Solid-Wall Boundary Condition of $\omega$ in the $k-\omega$-Typr
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institution = "Lab. of Aerodynamics, Dept. of Mech. Eng., Helsinki University of Technology",
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annote = "Haengmappar Exp: H" ,
author = "M. V. Heitor and G. P. Almeida" ,
title = "Turbulent Flows Over Curved Surfaces" ,
institution = "Instituto Superior T{\'e}cnico" ,
address = "Technical University of Lisbon" ,
year = 1995 }
@conference{ atkinson:castro:91 ,
author = "K. N. Atkinson and I. P. Castro" ,
title = "Computations of a Separated Turbulent Boundary
Layer" ,
booktitle = "Eighth Symp. on Turbulent Shear Flows",
address = "Techn. Univ. Munich" ,
year = 1991 }
@article{wilcox:88 ,
annote = "Haengmappar Turbulens: W" ,
author = "D. C. Wilcox" ,
title = "Reassessment of the Scale-determining Equation" ,
journal = aiaa,
volume = 26 ,
number = 11 ,
pages = "1299-1310" ,
year = 1988}
@article{ lien:leschziner:94 ,
annote = "Haengmappar Turbulens: LIEN & LESCHZINER" ,
author = "F. S. Lien and M. A. Leschziner" ,
title = "Assessment of Turbulence-transport Models
Including Non-Linear RNG Eddy Viscosity Formulation
and Second-Moment Closure for Flow Over a
Backward-Facing Step" ,
journal = cfluid,
volume = 23 ,
number = 8 ,
pages = "983-1004" ,
year = 1994 }
@article{ canuto:94 ,
annote = "LES",
author = "V. M. Canuto" ,
title = "Large Eddy Simulation of Turbulence: A Subgrid
Scale Model Including Shear, Vorticity, Rotation and Buoyancy" ,
journal = "Astrophysical J.",
volume = 428 ,
pages = "729-752" ,
year = 1994}
@article{ johansson:hallback:94 ,
annote = "Haengmappar Turbulens: J" ,
author = "A. V. Johansson and M. Hallb{\"a}ck" ,
title = "Modelling of Rapid Pressure-strain in
{R}eynolds-Stress Closures" ,
journal = jfm,
volume = 269 ,
pages = "143-168" ,
year = 1994 }
@techreport{ simpson:85 ,
annote = "Haengmappar Turbulens: S",
author = "R. L. Simpson" ,
title = "Two-dimensional Turbulent Separated Flow" ,
institution = "AGARD",
type = "Agardograph No 287 Vol 1" ,
year = 1985 }
@phdthesis{ groth:91 ,
annote = "Haengmappar Turbulens: G" ,
author = "J. Groth" ,
title = "On the Modelling of Homogeneous Turbulence" ,
school = "Royal Institute of Technology" ,
address = "Dept. of Mechanics{,} Stockholm{,} Sweden" ,
year = 1991 }
@techreport{ kadja:leschziner:87 ,
annote = "Haengmappar Turbulens: K",
author = "M. Kadja and M. A. Leschziner" ,
title = "The {``Team-COG''} Computer Code" ,
institution = "UMIST, Mechanical Engineering Dept.",
type = "November" ,
year = 1987 }
@article{ johnson:patel:93 ,
annote = "Haengmappar Turbulens: J (Experimental paper)",
author = "A. Johnson and V. C. Patel" ,
title = "Skin-friction Topology Over a Surface Mounted
Semi-Ellipsoidal Wing at Incidence" ,
journal = aiaa,
volume = 31 ,
number = 10 ,
pages = "1842-1849" ,
year = 1993}
@article{ pope:94 ,
annote = "Haengmappar Turbulens: P" ,
author = "S. B. Pope" ,
title = "On the Relationship Between Stochastic Lagrangian
Models of Turbulence and Second Moment Closures" ,
journal = pha,
volume = 6 ,
number = 2 ,
pages = "973-985" ,
year = 1994 }
@article{ pumir:94 ,
annote = "Haengmappar Turbulens: P" ,
author = "A. Pumir" ,
title = "A Numerical Study of Pressure Fluctuations in
Three-Dimensional{,} Incompressible{,}
Homogeneous{,} IsoTropic Turbulence" ,
journal = pha,
volume = 6 ,
number = 6 ,
pages = "2071-2083" ,
year = 1994 }
@article{ patel:chen:86 ,
annote = "Haengmappar Turbulens: P" ,
author = "V. C. Patel and H. C. Chen" ,
title = "Flow Over Tail and in Wake of Axisymmetric
Bodies: Review of State of the Art" ,
journal = "J. Ship Research",
volume = 30 ,
number = 3 ,
pages = "201-214" ,
year = 1986 }
@article{ patel:chon:yoon:91 ,
annote = "Haengmappar Turbulens: P" ,
author = "V. C. Patel and J. T. Chon and J.Y. Yoon" ,
title = "Turbulent Flow in a Channel With a Wavy Wall" ,
journal = "J. Fluids Eng.",
volume = 113 ,
pages = "579-586" ,
year = 1991}
@article{ patel:rodi:85 ,
annote = "Haengmappar Turbulens: P" ,
author = "V. C. Patel and W. Rodi and G. Scheuerer" ,
title = "Turbulence Models for Near-wall and Low {R}eynolds
Number Flows: A Review" ,
journal = aiaa,
volume = 23 ,
pages = "1308-1319" ,
year = 1985 }
@techreport{ piomelli:zang:90 ,
annote = "Haengmappar Turbulens: P",
author = "U. Piomelli and T. A. Zang" ,
title = "Large-Eddy Simulation of Transitional Channel Flow" ,
institution = "NASA",
type = "CR-187465 ICASE report No.90-80" ,
year = 1990 }
@article{ park:chung:89 ,
annote = "Haengmappar Turbulens: P" ,
author = "S. W. Park and M. K. Chung" ,
title = "Curvature-dependent Two-equation Model for
Prediction of Turbulent Recirculating Flows" ,
journal = aiaa,
volume = 27 ,
number = 3 ,
pages = "340-344" ,
year = 1989}
@article{ obi:peric:91 ,
annote = "Haengmappar Turbulens: O" ,
author = "S. Obi and M. Peri{\'c}" ,
title = "Second-moment Calculation Procedure for Turbulent
fFows with Collocated Variable Arrangement" ,
journal = aiaa,
volume = 29 ,
number = 4 ,
pages = "585-590" ,
year = 1991}
@article{ neves:moin:moser:94 ,
annote = "Haengmappar Turbulens: N" ,
author = "J. C. Neves and P. Moin and R. D. Moser" ,
title = "Effects of Convex Transverse Curvature on Wall
Bounded Turbulence. Part 1. The Velocity and Vorticity" ,
journal = jfm,
volume = 272 ,
pages = "349-381" ,
year = 1994 }
@article{ neves:moin:94 ,
annote = "Haengmappar Turbulens: N" ,
author = "J. C. Neves and P. Moin" ,
title = "Effects of Convex Transverse Curvature on Wall
Bounded Turbulence. Part 2. The Pressure Fluctuations" ,
journal = jfm,
volume = 272 ,
pages = "383-406" ,
year = 1994 }
@article{ nakamura:93 ,
annote = "Haengmappar Turbulens: N" ,
author = "Y. Nakamura" ,
title = "Bluff-body Aerodynamics and Turbulence" ,
journal = "J. Wind Eng. and Ind. Aerodyn.",
volume = 49 ,
pages = "65-78" ,
year = 1993}
@article{ menter:94 ,
annote = "Haengmappar Turbulens: M" ,
author = "F. R. Menter" ,
title = "Two-equation Eddy-viscosity Turbulence Models for
Engineering Applications" ,
journal = aiaa,
volume = 32 ,
pages = "1598-1605" ,
year = 1994}
@article{ mansour:kim:moin:89 ,
annote = "Haengmappar Turbulens: M" ,
author = "N. N. Mansour and J. Kim and P. Moin" ,
title = "Near-wall {$k$-$\varepsilon$}-turbulence Modeling" ,
journal = aiaa,
volume = 27 ,
pages = "1068-1073" ,
year = 1989}
@article{mansour:kim:moin:88,
annote = "Haengmappar Turbulens: M" ,
author = "N. N. Mansour and J. Kim and P. Moin" ,
title = "Reynolds-stress and Dissipation-Rate Budgets in a
Turbulent Channel Flow" ,
journal = jfm,
volume = 194 ,
pages = "15-44" ,
year = 1988}
@article{ lin:reed:93 ,
annote = "Haengmappar Turbulens: L" ,
author = "R.-S. Lin and H. L. Reed" ,
title = "Effect of Curvature on Stationary Crossflow
Instability of a Three-Dimensional Boundary Layer" ,
journal = aiaa,
volume = 31 ,
number = 9 ,
pages = "1611-1617" ,
year = 1993}
@article{ liu:zheng:94 ,
annote = "Haengmappar Turbulens: L" ,
author = "F. Liu and X. Zheng" ,
title = "Staggered Finite Volume Scheme for Solving
Cascade Flow With a {$k$-$\omega$} Turbulence Model" ,
journal = aiaa,
volume = 32 ,
number = 8 ,
pages = "1589-1597" ,
year = 1994}
@article{ laun:spalding:74 ,
annote = "Haengmappar Turbulens: LAUNDER" ,
author = "B. E. Launder and D. B. Spalding" ,
title = "The Numerical Computation of Turbulent Flows" ,
journal = "Computer Methods in Applied Mech. and Eng.",
volume = 3 ,
pages = "269-289" ,
year = 1974 }
@conference{ ramnefors:perzon:davidson:94 ,
author = "M. Ramnefors and S. Perzon and L. Davidson" ,
title = "Accuracy in Drag Predictions on Automobiles" ,
booktitle = "Vehicle aerodynamics",
address = "Loughborough Univ. of Techn. 18-19 July, UK" ,
year = 1994 }
@article{ leschz:rodi:81 ,
annote = "Haengmappar Turbulens: Leschziner" ,
author = "M. A. Leschziner and W. Rodi" ,
title = "Calculation of Annular and Twin Parallel Jets
Using Various Discretization Schemes and
Turbulence-model Variations" ,
journal = "J. Fluids Eng.",
volume = 103 ,
pages = "352-360" ,
year = 1981}
@conference{ lien:leschz:91 ,
annote = "Haengmappar Turbulens: LIEN & LESCHZINER" ,
author = "F. S. Lien and M. A. Leschziner" ,
title = "Second-moment Modelling of Recirculating Flow With
a Non-orthogonal Collocated Finite Volume
Algorithm" ,
booktitle = "8th Symp. Turbulent Shear Flows",
address = "Technical University of Munich, Germany" ,
month = "September" ,
year = 1991}
@article{ jimenez:94 ,
annote = "Haengmappar Turbulens: J" ,
author = "J. Jim{\'e}nez" ,
title = "On the Structure and Control of Near Wall
Turbulence" ,
journal = pha,
volume = 6 ,
number = 2 ,
pages = "944-952" ,
year = 1994}
@conference{ jaw:chou:94 ,
annote = "Haengmappar Turbulens: J" ,
author = "S.-Y. Jaw and S.-K. Chou" ,
title = "Prediction of an Uniform Flow Past HSVA Tanker
With Two-Layer {$k$-$\varepsilon$} Turbulence
Model" ,
booktitle = "CFD Workshop of Flow Around Ship Hulls",
address = "Tokyo" ,
year = 1994 }
@conference{ sotir:patel:94 ,
annote = "Haengmappar Turbulens: S" ,
author = "F. Sotiropoulos and V. C. Patel" ,
title = "Second-moment Modelling for Ship-stern and Wake
Flows" ,
booktitle = "CFD Workshop of Flow Around Ship Hulls",
address = "Tokyo" ,
year = 1994 }
@conference{ van:kim:94 ,
annote = "Haengmappar Turbulens: v" ,
author = "S.-H. van and H.-T. Kim" ,
title = "Calculation of Viscous Flow Around HSVA and
Mystery Hull Forms" ,
booktitle = "CFD Workshop of Flow Around Ship Hulls",
address = "Tokyo" ,
year = 1994 }
@conference{ kim:choudhury:94 ,
annote = "Haengmappar Turbulens: K" ,
author = "S.-E. Kim and D. Choudhury" ,
title = "A Computational Study of Turbulent Flows Around
two double-body Ship Models" ,
booktitle = "CFD Workshop of Flow Around Ship Hulls",
address = "Tokyo" ,
year = 1994 }
@conference{ ju:94 ,
annote = "Haengmappar Turbulens: J" ,
author = "S. Ju" ,
title = "Calculation of Flow Around Ship Hulls for CFD
Workshop TOKYO 1994",
booktitle = "CFD Workshop of Flow Around Ship Hulls",
address = "Tokyo" ,
year = 1994 }
@article{ jones:launder:72 ,
annote = "Haengmappar Turbulens: J" ,
author = "W. P. Jones and B. E. Launder" ,
title = "The Prediction of Laminarization With a
Two-Equation Model of Turbulence" ,
journal = "Int. J. Heat Mass Transfer",
volume = 15 ,
pages = "301-314" ,
year = 1972 }
@article{ irwin:smith:75 ,
annote = "Haengmappar Turbulens: I" ,
author = "H. P. Irwin and P. A. Smith" ,
title = "Prediction of the Effect of Streamline Curvature
on Turbulence" ,
journal = ph,
volume = 18 ,
number = 6 ,
pages = "624-630" ,
year = 1975}
@article{ villermaux:gagne:94 ,
annote = "Haengmappar Turbulens: V" ,
author = "E. Villermaux and Y. Gagne" ,
title = "Line Dispersion in Homogeneous Turbulence:
Stretching{,} Fractal Dimensions and Micromixing" ,
journal = "Phys. Review Letters",
volume = 73 ,
number = 2 ,
pages = "252-255" ,
year = 1994 }
@article{ soto:94 ,
annote = "Haengmappar Turbulens: S" ,
author = "J. L. C. soto and M. C. C. canalejo and beltr{\'a}n
M. M. and G{\'O}MEZ-NIETO M. A." ,
title = "Numerical Analysis of the M. P. P. Model of
Turbulence" ,
journal = "Computers Math. Applic.",
volume = 27 ,
pages = "17-28" ,
year = 1994 }
@article{ brors:eidsvik:94 ,
annote = "Haengmappar Turbulens: B" ,
author = "B. Br{\o}rs and K. J. Eidsvik" ,
title = "Oscillatory Boundary Layer Flows Modelled With
Dynamic {R}eynolds Stress Turbulence Closure" ,
journal = "Continental Shelf Research",
volume = 14 ,
number = "13/14" ,
pages = "1455-1475" ,
year = 1994 }
@article{ briscolini:santangelo:94 ,
annote = "Haengmappar Turbulens: B" ,
author = "M. Briscolini and P. Santangelo" ,
title = "The Non-Gaussian Statistics of the Velocity Field
in Low-Resolution Large-Eddy Simulations of
homogeneous turBulence" ,
journal = jfm,
volume = 270 ,
pages = "199-217" ,
year = 1994 }
@article{ antonia:kim:94 ,
annote = "Haengmappar Turbulens: A" ,
author = "R. A. Antonia and J. Kim" ,
title = "A Numerical Study of Local Isotropy of Turbulence",
journal = pha,
volume = 6 ,
number = 2 ,
pages = "834-841" ,
year = 1994}
@article{ bernard:rovelstad:94 ,
annote = "Haengmappar Turbulens: B" ,
author = "P. S. Bernard and A. L. Rovelstad" ,
title = "On the Physical Accuracy of Scalar Transport
Modeling in Inhomogeneous Turbulence" ,
journal = pha,
volume = 6 ,
number = 9 ,
pages = "3093-3108" ,
year = 1994}
@conference{ hochbaum:93 ,
author = "A. C. Hochbaum and P. Sames and J. Kux" ,
title = "Turbulent Flow Around Ship Hulls" ,
booktitle = "Workshop on ships",
year = 1993 }
@article{ hanjalic:laun:72 ,
annote = "Haengmappar Turbulens: h" ,
author = "K. Hanjali{\'c} and B. E. Launder" ,
title = "A {R}eynolds Stress Model of Turbulence and Its
Application to Thin Shear Flows" ,
journal = jfm,
volume = 52,
pages = "609--638" ,
year = 1972}
@article{ cheng:canuto:94 ,
annote = "Haengmappar Turbulens: C" ,
author = "Y. Cheng and V. M. Canuto" ,
title = "Stably Stratified Shear Turbulence: A New Model
for the Energy Dissipation Length Scale" ,
journal = "J. of the Atmospheric Sciences",
volume = 51 ,
number = 16 ,
pages = "2384-2396" ,
year = 1994}
@article{ bradshaw:94 ,
annote = "Haengmappar Turbulens: B" ,
author = "P. Bradshaw" ,
title = "Turbulence: the Chief Outstanding Difficulty of
our Subject" ,
journal = "Experiments in Fluids",
volume = 16 ,
pages = "203-216" ,
year = 1994}
@article{ dengel:90 ,
annote = "Haengmappar Experiments: D" ,
author = "P. Dengel and H. H. Fernholz" ,
title = "An Experimental Investigation of an
Incompressible Turbulent Boundary Layer in the
Vicinity of Separation" ,
journal = jfm,
volume = 212 ,
pages = "615-636" ,
year = 1990}
@article{ pancha:lumley:93 ,
annote = "Haengmappar Turbulens: P" ,
author = "N. R. Panchapakesan and J. L. Lumley" ,
title = "Turbulence Measurements in Axisymmetric Jets of
Air and Helium. Part 1. Air Jet" ,
journal = jfm,
volume = 246 ,
pages = "197-223" ,
year = 1993 }
@article{ bruin:93 ,
annote = "Haengmappar Turbulens: B" ,
author = "A. C. Bruin and L. H. J. Absil and D. M. Passchier" ,
title = "Turbulence Modelling of the Shear Layers in the
Trailing Edge Region of a Modern Rear-loaded
Airfoil at Incidence" ,
journal = "Appl. Sc. Research",
volume = 51 ,
pages = "483-488" ,
year = 1993 }
@conference{ shima:95 ,
annote = "Haengmappar Turbulens: S" ,
author = "N. Shima" ,
title = "Modeling of Asymptotic Near-wall Behaviour of
the {R}eynolds Stress Dissipation" ,
booktitle = "10th Symp. Turbulent Shear Flows",
address = "The Pennsylvania State University, USA" ,
month = "August 14-16" ,
year = 1995}
@conference{ lien:leschz:95 ,
annote = "Haengmappar Turbulens: LIEN & LESCHZINER" ,
author = "F. S. Lien and M. A. Leschziner" ,
title = "Computational Modelling of Multiple Vortical
Separation From Streamlined Body at High Incidence" ,
booktitle = "10th Symp. Turbulent Shear Flows",
address = "The Pennsylvania State University, USA" ,
month = "August" ,
year = 1995}
@conference{ craft:laun:95 ,
annote = "Haengmappar Turbulens: C" ,
author = "T. J. Craft and B. E. Launder" ,
title = "Improvements in Near Wall {R}eynolds Stress
Modelling for Complex Flow Geometries" ,
booktitle = "10th Symp. Turbulent Shear Flows",
address = "The Pennsylvania State University, USA" ,
month = "August" ,
year = 1995}
@conference{ craft:laun:suga:95 ,
annote = "Haengmappar Turbulens: C" ,
author = "T. J. Craft and B. E. Launder and K. Suga" ,
title = "A Non-linear Eddy Viscosity Model Including
Sensitivity to Stress Anisotropy" ,
booktitle = "10th Symp. Turbulent Shear Flows",
address = "The Pennsylvania State University, USA" ,
month = "August" ,
year = 1995}
@conference{ Jakirlic:hanjalic:95 ,
annote = "Haengmappar Turbulens: J" ,
author = "S. Jakirli{\'c} and K. HANJALI{\'C} K." ,
title = "A Second-moment Closure for Non-equilibrium and
Separating High- and Low-Re-number Flows" ,
booktitle = "10th Symp. Turbulent Shear Flows",
address = "The Pennsylvania State University, USA" ,
month = "August" ,
year = 1995}
@article{ lien:leschz:94 ,
annote = "Haengmappar Turbulens: LIEN & LESCHZINER" ,
author = "F. S. Lien and M. A. Leschziner" ,
title = "A General Non-orthogonal Collocated Finite Volume
Algorithm for Turbulent Flow at All Speeds
Incorporating Second-moment Turbulence-Transport
Closure{,} Part 1: Computational Implementation" ,
journal = "Comput. Methods Appl. Mech. Engrg.",
volume = 114,
pages = "123-148" ,
year = 1994}
@article{ lien:leschz:94 ,
annote = "Haengmappar Turbulens: LIEN & LESCHZINER" ,
author = "F. S. Lien and M. A. Leschziner" ,
title = "A General Non-orthogonal Collocated Finite Volume
Algorithm for Turbulent Flow at All Speeds
Incorporating Second-moment Turbulence-Transport
Closure{,} Part 2: Application" ,
journal = "Comput. Methods Appl. Mech. Engrg.",
volume = 114,
pages = "149-167" ,
year = 1994}
@phdthesis{ craft:91 ,
annote = "Bokhyllan" ,
author = "T. J. Craft" ,
title = "Second Moment Modeling of Scalar Transport" ,
school = "Univ. of Manchester" ,
address = "Faculty of Technology{,} Manchester{,}
England{,} UK" ,
year = 1991}
@article{ gibson:younis:86 ,
annote = "Haengmappar Turbulens: G" ,
author = "M. M. Gibson and B. A. Younis" ,
title = "Calculation of Boundary Layers With Sudden Transverse
Strain" ,
journal = "J. Fluids Eng.",
volume = 108 ,
pages = "470-475" ,
year = 1986}
@article{ lrr:75 ,
annote = "Haengmappar Turbulens: LAUNDER" ,
author = "B. E. Launder and G. J. Reece and W. Rodi" ,
title = "Progress in the Development of a {R}eynolds-stress
Turbulence Closure" ,
journal = jfm,
volume = 68 ,
number = 3 ,
pages = "537-566" ,
year = 1975}
@article{ kolov:vatutin:72 ,
annote = "Haengmappar Turbulens: K" ,
author = "B. A. Kolovandin and I. A. Vatutin" ,
title = "Statistical Transfer Theory in Non-homogeneous Turbulence" ,
journal = "Int. J. Heat Mass Transfer",
volume = 15 ,
pages = "2371-2383" ,
year = 1972}
@article{ jova:ye:durst:95 ,
annote = "Haengmappar Turbulens: J" ,
author = "J. Jovanovi{\'c} and Q.-Y. Ye and F. Durst" ,
title = "Stastitical Interpretation of the Turbulent Dissipation
Rate in Wall-bounded Flows" ,
journal = jfm,
volume = 293 ,
pages = "321-347" ,
year = 1995}
@article{ lai:so:90 ,
annote = "Haengmappar Turbulens: L" ,
author = "Y. G. Lai and R. M. C. So" ,
title = "On Near-wall Turbulent Flow Modelling" ,
journal = jfm,
volume = 221 ,
pages = "641-673" ,
year = 1990}
@article{ launder:shima:89 ,
annote = "Haengmappar Turbulens: LAUNDER",
author = "B. E. Launder and N. Shima" ,
title = "Second-Moment Closure for the Near-Wall Sublayer{:}
Development and Application" ,
journal = aiaa,
volume = 27 ,
pages = "1319-1325" ,
year = 1989}
@article{ shima:88 ,
annote = "Haengmappar Turbulens: S",
author = "N. SHIMA." ,
title = "A {R}eynolds-Stress Model for Near-Wall and
Low-{R}eynolds-Number Regions" ,
journal = "J. Fluids Eng.",
volume = 110 ,
pages = "38-44" ,
year = 1988}
@article{ so:lai:zhang:91 ,
annote = "Haengmappar Turbulens: S" ,
author = "R. M. C. So and Y. G. Lai and H. S. Zhang" ,
title = "Second-Order Near-Wall Turbulence Closures{:} a Review" ,
journal = aiaa,
volume = 29 ,
pages = "1819-1835" ,
year = 1991}
@article{ so:lai:90 ,
annote = "Haengmappar Turbulens: S" ,
author = "R. M. C. So and Y. G. Lai" ,
title = "Near-Wall Turbulence Closure for Curved Flows" ,
journal = aiaa,
volume = 29 ,
pages = "1202-1213" ,
year = 1990}
@inproceedings{ kim:93 ,
annote = "Haengmappar Turbulens: K" ,
author = "K.Y. Kim" ,
title = "A Second-order Closure for Near-wall Turbulence",
publisher = "Elsevier Science Publishers B.V." ,
pages = "125-134" ,
year = 1993}
@inproceedings{ sotir:patel:93 ,
annote = "Haengmappar Turbulens: S" ,
author = "F. Sotiropoulos and V. C. Patel" ,
title = "Evaluation of Some Near-wall Models for the {R}eynolds
Stress Transport Equations in a Complex 3-D Shear Flow" ,
booktitle = "Near-wall Turbulent Flows",
publisher = "Elsevier Science Publishers B.V." ,
pages = "987-997" ,
year = 1993}
@conference{ hallback:93 ,
annote = "Haengmappar Turbulens: H" ,
author = "M. Hallb{\"a}ck and T. Sj{\"o}gren and A. Johansson" ,
title = "Modeling of Intercomponent Transfer in {R}eynolds
Stress Closures of Homogeneous Turbulence" ,
booktitle = "NINTH SYMPOSIUM ON ''Turbulent Shear Flows'' ",
address = "Kyoto{,} Japan" ,
date = "August 16-18" ,
year = 1993}
@article{ davydov:61 ,
annote = "Haengmappar Turbulens: D" ,
author = "B. I. Davydov" ,
title = "On the Statistical Dynamics of an Incompressible
Turbulent Fluid" ,
journal = "Dok. Akad. Nauk SSSR",
volume = 136 ,
pages = "47-50" ,
year = 1961}
@techreport{so:yoo:86 ,
annote = "Haeng mappar. Turbulens: S" ,
author = "R. M. C. so and G. J. yoo" ,
title = "On the Modeling of Low-{R}eynolds-Number Turbulence" ,
institution = "NASA",
type = "Contractor Rept 3994" ,
year = 1986}
@article{ park:sung:95 ,
annote = "Haeng mappar. Turbulens: P" ,
author = "T. S. Park and H. J. Sung" ,
title = "A Nonlinear Low-{R}eynolds-number $k$-$\varepsilon$
Model for Turbulent Separated and Reattaching
Flows - I. Flow Field Computations" ,
journal = "Int. J. Heat Mass Transfer",
volume = 38 ,
number = 14 ,
pages = "2657-2666" ,
year = 1995}
@article{craft:laun:92 ,
annote = "Haeng mappar. Turbulens: C" ,
author = "T. J. Craft and B. E. Launder" ,
title = "Near Wall-Reflection Model Applied to the
Turbulent ImpinGing Jet" ,
journal = aiaa,
volume = 30 ,
number = 12 ,
pages = "2970-2972" ,
year = 1992}
@manual{f3d:man ,
annote = "Bok-hyllan" ,
title = "CFDS-FLOW3D 3.3 User Guide" ,
organization = "AEA Technology" ,
address = "Harwell Laboratory, UK" ,
year = 1994}
@techreport{f3d:rsm ,
annote = "Haeng mappar. Turbulens: C" ,
author = "D. S. Clarke and N. S. Wilkes" ,
title = "The Calculation of Turbulent Flows in Complex
Geometries Using a Differential Stress Model" ,
institUtion = "AEA Technology" ,
note = "AERE-R 13428" ,
year = 1989}
@article{launder:sharma:74 ,
annote = "Haeng mappar. Turbulens: LAUNDER" ,
author = "B. E. Launder and B. T. Sharma" ,
title = "Application of the Energy Dissipation Model of
Turbulence to the Calculation of Flow Near a
Spinning Disc" ,
journal = "Lett. Heat and Mass Transfer" ,
volume = 1,
pages = "131-138",
year = 1974}
@article{hl:76 ,
annote = "Haeng mappar. Turbulens: H" ,
author = "K. Hanjali\'c and B. E. Launder" ,
title = "Contribution Towards a {R}eynolds-stress Closure for
Low-{R}eynolds-Number Turbulence" ,
journal= jfm,
volume = 74 ,
pages = "593-610" ,
year = 1976}
@article{naot:70 ,
annote = "Har jag ej." ,
author = "D. Naot and A. Shavit and M. Wolfshtein" ,
title = "Interactions Between Components of the Turbulent
Velocity Correlation Tensor" ,
journal= "Israel J. Techn.",
volume = 8 ,
pages = "259" ,
year = 1970}
@article{rotta:51 ,
annote = "Haeng mappar. Turbulens: R" ,
author = "J. C. Rotta" ,
title = "Statistische Theorie Nichthomogener Turbulenz" ,
journal= "Zeitschrift f{\"u}r Physik" ,
volume = 129 ,
pages = "547-572" ,
year = 1951}
@article{gibson:launder:78 ,
annote = "Haeng mappar. Turbulens: G" ,
author = "M. M. Gibson and B. E. Launder" ,
title = "Ground Effects on Pressure Fluctuations in the Atmospheric
Boundary Layer" ,
journal= jfm,
volume = 86 ,
pages = "491-511" ,
year = 1978}
@article{almeida:93 ,
annote = "Haeng mappar. Exp: A" ,
author = "M. V. Almeida and D. F. G. Durau and M. V. Heitor" ,
title = "Wake Flows Behind Two-dimensional Hills" ,
journal= "Exp. Thermal and Fluid Science" ,
volume = 7 ,
pages = "87" ,
year = 1993}
@techreport{laufer:52 ,
annote = "Haeng mappar. Exp: L" ,
author = "J. Laufer" ,
title = "Investigation of Turbulent Flow in a Two-dimensional
Channel" ,
note = "Rept. 1053" ,
institution = "California Institute of Technology" ,
year = 1952}
@techreport{huang:76 ,
annote = "Haeng mappar. Exp: H" ,
author = "T. T. Huang and H. T. Wang and N. Santelli and N. C. Groves" ,
title = "Propeller/Stern/Boundary Layer Interaction on Axisymmetric
Bodies. Theory and Experiment." ,
institution = "David W. Taylor Naval Ship Research and Development
Center{,} Ship performance dept." ,
type = "Research and development rept." ,
year = 1976}
@article{daly:70 ,
annote = "Haeng mappar. Turbulens: D" ,
author = "B. J. Daly and F. H. Harlow" ,
title = "Transport Equation in Turbulence" ,
journal = ph,
volume = 13 ,
pages = "2634-2649" ,
year = 1970}
@article{chung:park:87,
annote = "Haeng mappar. Turbulens: C" ,
author = "M. K. Chung and S. W. Park and K. C. Kim",
title = "Curvature Effect on Third-order Velocity
Correlations and Its Model Representation" ,
journal = ph,
volume = 30 ,
pages = "626-628" ,
year = 1987}
@article{park:chung:91 ,
annote = "Haeng mappar. Turbulens: P" ,
author = "S. B. Park and M. K. Chung and D. H. Choi" ,
title = "Reynolds{-}Stress Model Analysis of Turbulent Flow
Over a Curved Axisymmetric Body" ,
journal = aiaa,
volume = 29 ,
number = 4 ,
pages = "591-594" ,
year = 1991 }
@conference{johansson:davidson:94 ,
author = "P. Johansson and L. Davidson",
title = "A Full Multigrid Method Applied to Turbulent Flow
Using the {SIMPLEC} Algorithm Together With a Collocated Arrangement",
booktitle = "Multigrid Methods IV" ,
publisher = "Birkh{\"a}user Verlag" ,
pages = "245-256" ,
year = 1994 }
@article{johansson:davidson:95 ,
author = "P. Johansson and L. Davidson",
title ="Modified Collocated SIMPLEC Algorithm Applied to Buoyancy-affected
Turbulent Flow Using a Multigrid Solution Procedure",
journal = nhtb,
volume = 28 ,
pages = "39-57" ,
year = 1995 }
@article{gresho:sani:87 ,
author = "P. Gresho and R. Sani",
title ="On Pressure Boundary Conditions for the
Incompressible {N}avier-{S}tokes Equations",
journal = "Int. J. Num. Meth in Fluids " ,
volume = 7 ,
pages = "1111-1145" ,
year = 1987 }
@techreport{brandt:84 ,
author = "A. Brandt",
title = " Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics",
booktitle = "Computational Fluid Dynamics Lecture Notes" ,
institution = "Von-Karman Institute",
year = 1984}
@techreport{stuben:92,
author = "A. Brandt and W. Joppich and J. Linden and G. Lonsdale and
Sch{\"u}ller and B. Steckel and K. St{\"u}ben",
title = " Arbeitspapiere Der GMD 690",
institution = "Gesellschaft f{\"u}r mathematik und datenverarbeitung" ,
year = 1992}
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{ kite_colour L draw_tile }ifelse
pop } bind def
/half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
-144 rotate Ll neg 0 translate half_dart grestore }
{ dart_colour l draw_tile }ifelse
pop } bind def
/kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
border_width setlinewidth 1 setlinejoin 1 setlinecap
% 450 0 translate
dup f exch neg exp dup scale
5 {kite 72 rotate } repeat stroke
grestore
} def
%
%
/TruchetFill { % on stack: scaling factor
10 dict begin
dup dup scale
1 exch div round /penroseFactor ED
a 0 dtransform round exch round exch
2 copy idtransform
exch Atan rotate
idtransform pop /a ED
.25 .25 itransform pathbbox
/y2 ED
a Div ceiling cvi /x2 ED /y1 ED
a Div cvi /x1 ED /y2 y2 y1 sub def
clip
newpath
systemdict
/setstrokeadjust known { true setstrokeadjust } if
/ma a neg def
/ha a 2 div def
/mha ha neg def
/tile {
rand dup 2 idiv 2 mul eq { 90 rotate } if
mha mha moveto ha mha lineto
ha ha lineto mha ha lineto
% closepath .1 setlinewidth stroke
contents
} def
/contents{
0 ha moveto ha 0 lineto
0 mha moveto mha 0 lineto
% 1 setlinewidth stroke
} def
/dotiling {
f ma mul a f a mul {
/i exch def
f ma mul a f a mul {
/j exch def
gsave i j translate
tile stroke grestore
} for
} for
} def
%
/f 3 def
5 srand dotiling
end % local user dict
} def
%
/BeginArrow {
ADict begin % hold it local, for end see EndArrow
/@mtrx CM def
gsave
2 copy T
2 index sub neg exch
3 index sub exch Atan
rotate newpath
} def
%
/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
%
/Arrow {
CLW mul add dup
2 div /w ED
mul dup /h ED
mul /a ED
{ 0 h T 1 -1 scale } if
w neg h moveto
0 0 L w h L w neg a neg rlineto
gsave fill grestore
} def
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
CLW mul add dup
2 div /w ED
mul dup /h ED
mul /Inset ED
{ 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
w neg h moveto % lower left of >
w 9 div 4 mul neg h 3 div 2 mul
w 9 div neg h 3 div
0 0 curveto % tip of >
w 9 div h 3 div
w 9 div 4 mul h 3 div 2 mul
w h curveto % upper left of >
w neg Inset neg rlineto % move to x=0 and inset
gsave fill grestore
} def
%
/Tbar {
CLW mul add /z ED
z -2 div CLW 2 div moveto
z 0 rlineto stroke
0 CLW moveto
} def
%
/Bracket {
CLW mul add dup CLW sub 2 div
/x ED mul CLW add /y ED /z CLW 2 div def
x neg y moveto
x neg CLW 2 div L x CLW 2 div L x y L stroke
0 CLW moveto
} def
%
/RoundBracket {
CLW mul add dup 2 div
/x ED mul /y ED /mtrx CM def
0 CLW 2 div T x y mul 0 ne { x y scale } if
1 1 moveto
.85 .5 .35 0 0 0 curveto
-.35 0 -.85 .5 -1 1 curveto
mtrx setmatrix stroke 0 CLW moveto
} def
%
/SD { 0 360 arc fill } def
%
/EndDot { % DS is the dot size
{ /z DS def } { /z 0 def } ifelse % outer or inner dimen
/b ED % the color definition
0 z DS SD
b { 0 z DS CLW sub SD } if
0 DS z add CLW 4 div sub
moveto
} def
%
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
load } if ] cvx newpath 3 1 roll T exec } def
%
/NArray { % holds the coordinates and on top of stack the showpoints boolean
/showpoints ED
counttomark 2 div dup cvi /n ED % n 2 div on stack
n eq not { exch pop } if % even numbers of points? delete one
] aload /Points ED
showpoints not { Points aload pop } if
% { ] aload /Points ED }
% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
} def
%
/Line {
NArray n 0 eq not
{ n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
n { Lineto } repeat
CP 4 2 roll ArrowB L pop pop
} if
} def
%
/LineToYAxis {
/Ox ED % Save the x origin value
NArray % all x-y pairs on stack
n { 2 copy moveto % go to current point
Ox exch Lineto % line to y-axis
pop % delete old x-value
} repeat
} def
%
/LineToXAxis{
/Oy ED % Save the y origin value
NArray % all x-y pairs on stack
n 0 eq not
{ n 1 eq { 0 0 /n 2 def } if
ArrowA
/n n 2 sub def
CP 2 copy moveto pop Oy Lineto
n { 2 copy moveto pop Oy Lineto } repeat
CP
4 2 roll
ArrowB
2 copy moveto pop Oy
L
pop pop } if
} def
%
/Arcto {
/a [ 6 -2 roll ] cvx def
a r
/arcto load stopped { 5 } { 4 } ifelse { pop } repeat
a
} def
%
/CheckClosed {
dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
and { pop pop /n n 1 sub def } if
} def
%
/Polygon {
NArray n 2 eq { 0 0 /n 3 def } if
n 3 lt
{ n { pop pop } repeat }
{ n 3 gt { CheckClosed } if
n 2 mul -2 roll
/y0 ED /x0 ED /y1 ED /x1 ED
x1 y1
/x1 x0 x1 add 2 div def
/y1 y0 y1 add 2 div def
x1 y1 moveto
/n n 2 sub def
n { Lineto } repeat
x1 y1 x0 y0 6 4 roll Lineto
Lineto pop pop closepath } ifelse
} def
%
/SymbolPolygon { % on stack [ x y x y ...
counttomark % number of elements
2 add /m ED
2 copy m 2 roll % copy last two
m 2 div cvi /n ED % n pairs
/YA ED /XA ED % the start point
n 1 sub {
/YB ED /XB ED
/XLength XB XA sub def
/YLength YB YA sub def
/PAngle YLength XLength Atan def
/XYLength XLength YLength Pyth def
/nSym XYLength SymStep Div cvi def
/Shift Symbol stringwidth pop 2 Div def
/deltaX XLength nSym Div def
/deltaY YLength nSym Div def
XA Shift sub YA Shift sub moveto
nSym {
gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
Symbol show
grestore
deltaX deltaY rmoveto
} repeat
% XB Shift sub YB Shift sub moveto Symbol show
/YA YB def /XA XB def
} repeat
pop % delete the mark symbol
} def
%
/Diamond {
/mtrx CM def
T rotate
/h ED
/w ED
dup 0 eq { pop } { CLW mul neg
/d ED
/a w h Atan def
/h d a sin Div h add def
/w d a cos Div w add def } ifelse
mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
/ArrowA { moveto } def
/ArrowB { } def
false Line
closepath mtrx setmatrix } def
%
/Triangle {
/mtrx CM def
translate
rotate /h ED 2 div /w ED
dup CLW mul /d ED
/h h d w h Atan sin Div sub def
/w w d h w Atan 2 div dup cos exch sin Div mul sub def
mark
0 d w neg d 0 h w d 0 d
/ArrowA { moveto } def
/ArrowB { } def
false
Line
closepath
mtrx
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop
} def
% DG/SR modification end
%
/CCA {
/y ED /x ED
2 copy y sub /dy1 ED
x sub /dx1 ED
/l1 dx1 dy1 Pyth def
} def
%
/CC {
/l0 l1 def
/x1 x dx sub def
/y1 y dy sub def
/dx0 dx1 def
/dy0 dy1 def
CCA
/dx dx0 l1 c exp mul dx1 l0 c exp mul add def
/dy dy0 l1 c exp mul dy1 l0 c exp mul add def
/m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
/x2 x l0 dx mul m mul sub def
/y2 y l0 dy mul m mul sub def
/dx l1 dx mul m mul neg def
/dy l1 dy mul m mul neg def
} def
%
/IC {
/c c 1 add def
c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
/a a 2 mul 3 div 45 cos b exp div def
CCA
/dx 0 def
/dy 0 def
} def
%
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
/NC { CC x1 y1 x2 y2 x y curveto } def
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
/NAC { x2 y2 x y curveto CC x1 y1 } def
/EAC { x2 y2 x y ArrowB curveto pop pop } def
%
/OpenCurve {
NArray n 3 lt
{ n { pop pop } repeat }
{ BOC /n n 3 sub def n { NC } repeat EOC } ifelse
} def
%
/CurvePath {
%% for negative SymStep we calculate the distance
SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
0.5 setflat
flattenpath /z 0 def /z0 0 def
{ /y1 ED /x1 ED /y2 y1 def /x2 x1 def
x1 Shift sub y1 Shift sub moveto
gsave
curveticks
{ x1 y1 translate startAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{ startAngle rotate Symbol show }
ifelse
grestore /z0 z def }
{ /y ED /x ED PathLength@ z z0 sub SymStep ge {
x Shift sub y Shift sub moveto
gsave
curveticks
{ y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
x y translate rotAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{
rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
grestore /z0 z def } if
/yOld y def /xOld x def }
{} %% the lineto part
{ /y y2 def /x x2 def PathLength@
x Shift sub y Shift sub moveto
gsave
curveticks
{ y yOld sub x xOld sub Atan 180 sub /rotAngle ED
x y translate rotAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{
x Shift sub y Shift sub moveto
rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
grestore
}
pathforall
% curveticks
% { gsave
% x y translate rotAngle rotate
% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
% SymbolLinewidth setlinewidth stroke grestore
% } if
z
} def
%
/OpenSymbolCurve {
OpenCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/AltCurve {
{ false NArray n 2 mul 2 roll
[ n 2 mul 3 sub 1 roll ] aload
/Points ED
n 2 mul -2 roll }
{ false NArray } ifelse
n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
} def
%
/AltOpenSymbolCurve {
AltCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedCurve {
NArray n 3 lt
{ n { pop pop } repeat }
{ n 3 gt { CheckClosed } if
6 copy n 2 mul 6 add 6 roll
IC CC x y moveto n { NC } repeat
closepath pop pop
} ifelse
} def
%
/ClosedSymbolCurve {
ClosedCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/CalcBezierSpline {% Christoph Bersch
10 dict begin
/getX { Points exch 2 mul get } def
/getY { Points exch 2 mul 1 add get } def
/n Points length 1 sub 2 idiv def
/GetFirstControlPoints {
/x n array def
/tmp n array def
/b 2 def
x 0 rhs 0 get b div put
1 1 n 1 sub {
/i exch def
tmp i 1 b div dup 4 1 roll put
i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
x i rhs i get x i 1 sub get sub b div put
} for
1 1 n 1 sub {
n exch sub
dup dup x exch 1 sub 2 copy 6 2 roll
get 3 1 roll tmp exch get
exch x exch get mul sub
put
} for
x
} def
%
n 1 eq {
0 getX 2 mul 1 getX add 3 div
0 getY 2 mul 1 getY add 3 div
exch dup 3 1 roll 2 mul 0 getX sub
exch dup 3 1 roll 2 mul 0 getY sub
[ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
} {
/outPoints 6 n mul 2 add array def
0 1 n {
dup dup 6 mul dup 1 add
outPoints exch 5 -1 roll getY put
outPoints exch 3 -1 roll getX put
} for
/rhs n array def
1 1 n 2 sub {
rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
} for
rhs 0 0 getX 1 getX 2 mul add put
rhs n 1 sub dup getX 8 mul n getX add 2 div put
GetFirstControlPoints
1 1 n 2 sub {
rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
} for
rhs 0 0 getY 1 getY 2 mul add put
rhs n 1 sub dup getY 8 mul n getY add 2 div put
GetFirstControlPoints
0 1 n 1 sub {
/i exch def
2 copy
i get outPoints 6 i mul 3 add 3 -1 roll put
i get outPoints 6 i mul 2 add 3 -1 roll put
2 copy
i n 1 sub lt {
i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
}{
n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
} ifelse
} for
pop pop
} ifelse
outPoints
end
} def
/Spline {
/showpoints ED
counttomark 2 div dup cvi /n ED
n eq not { exch pop } if
] /Points ED
n 1 gt {
CalcBezierSpline
mark exch aload pop
ArrowA
n 2 sub {
6 2 roll 4 2 roll curveto
} repeat
6 2 roll 4 2 roll ArrowB curveto
} if
} def
/OpenSymbolSpline {
Spline
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
%
/FontDot {
DS 2 mul dup
matrix scale matrix concatmatrix exch matrix
rotate matrix concatmatrix exch
findfont exch makefont setfont
} def
%
/Rect {
x1 y1 y2 add 2 div moveto
% x1 y2 lineto
% x2 y2 lineto
% x2 y1 lineto
% x1 y1 lineto
x1 y1 lineto % counter clockwise path
x2 y1 lineto
x2 y2 lineto
x1 y2 lineto
closepath
} def
%
/OvalFrame {
x1 x2 eq y1 y2 eq or
{ pop pop x1 y1 moveto x2 y2 L }
{ y1 y2 sub abs x1 x2 sub abs 2 copy gt
{ exch pop } { pop } ifelse
2 div exch { dup 3 1 roll mul exch } if
2 copy lt { pop } { exch pop } ifelse
/b ED
x1 y1 y2 add 2 div moveto
x1 y2 x2 y2 b arcto
x2 y2 x2 y1 b arcto
x2 y1 x1 y1 b arcto
x1 y1 x1 y2 b arcto
16 { pop } repeat
closepath
} ifelse
} def
%
/Frame {
CLW mul /a ED
3 -1 roll
2 copy gt { exch } if
a sub /y2 ED
a add /y1 ED
2 copy gt { exch } if
a sub /x2 ED
a add /x1 ED
1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
} def
%
/BezierNArray {
/f ED
counttomark 2 div dup cvi /n ED
n eq not { exch pop } if
n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
} def
%
/OpenBezier {
BezierNArray
n 1 eq
{ pop pop }
{ ArrowA n 4 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
6 2 roll 4 2 roll ArrowB curveto } ifelse
} def
%
/OpenSymbolBezier {
OpenBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedBezier {
BezierNArray
n 1 eq
{ pop pop }
{ moveto n 1 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
closepath } ifelse
} def
%
/ClosedSymbolBezier {
/f ED % save showpoints value
2 copy /yEnd ED /xEnd ED
counttomark -2 roll 2 copy /yStart ED /xStart ED
counttomark 2 roll
f
ClosedBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
[ xEnd yEnd xStart yStart SymbolLine
} def
%
/BezierShowPoints {
gsave
Points aload length 2 div cvi /n ED
moveto
n 1 sub { lineto } repeat
CLW 2 div SLW [ 4 4 ] 0 setdash stroke
grestore
} def
%
/Parab {
/y0 ED /x0 ED /y1 ED /x1 ED
/dx x0 x1 sub 3 div def
/dy y0 y1 sub 3 div def
x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
} def
%
/Parab1 { % 1 end | 0 SP
/ySP ED /xSP ED /y1 ED /x1 ED
/dx xSP x1 sub 3 div def
/dy ySP y1 sub 3 div def
newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
x1 ySP lineto closepath clip
currentpoint
newpath moveto
xSP dx sub ySP dy add x1 y1 ArrowA
xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
} def
%
/Grid {
newpath
/a 4 string def
/b ED % psk@gridlabels in pt
/c ED % { \pst@usecolor\psgridlabelcolor }
/n ED % psk@griddots
cvi dup 1 lt { pop 1 } if
/s ED % \psk@subgriddiv
s div dup 0 eq { pop 1 } if
/dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
/dx ED dy div round dy mul % \pst@number\psxunit abs
/y0 ED dx div round dx mul
/x0 ED dy div round cvi
/y2 ED dx div round cvi
/x2 ED dy div round cvi
/y1 ED dx div round cvi
/x1 ED
/h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
/w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
b 0 gt {
/z1 b 4 div CLW 2 div add def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Helvetica findfont b scalefont setfont
% is set in pstricks.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% /NimbusSanL-Regu findfont b scalefont setfont
/b b .95 mul CLW 2 div add def } if
systemdict /setstrokeadjust known
{ true setstrokeadjust /t { } def }
{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
exch itransform } bind def } ifelse
gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
/i x1 def
/f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
/g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
dup % run loop two times: lines and labels
{ i dx mul dup xGridOffset add y0 moveto % draw the lines
dup t f moveto
g t L stroke
/i i w add def
} repeat
/i x1 def
GridDX div ceiling cvi
{ i dx mul GridDX mul dup xGridOffset add y0 moveto % plot the labels
b 0 gt
{ gsave c i GridDX mul a cvs dup stringwidth pop /z2 ED
w 0 gt {z1} {z1 z2 add neg} ifelse
h 0 gt {b neg}{z1} ifelse exch GridDX div z2 2 div sub exch
rmoveto show grestore } if
/i i w add def
} repeat
grestore
gsave
n 0 gt
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
{ 2 setlinecap } ifelse
/i y1 def
/f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
/g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
dup % run loop two times: lines and labels
{ newpath i dy mul dup yGridOffset add x0 exch moveto
dup f exch t moveto
g exch t L stroke
/i i h add def
} repeat
/i y1 def
GridDY div ceiling cvi
{ newpath i dy mul GridDY mul dup yGridOffset add x0 exch moveto
b 0 gt { gsave c i GridDY mul a cvs dup stringwidth pop
/z2 ED
w 0 gt {z1 z2 add neg} {z1} ifelse
h 0 gt {z1} {b neg} ifelse GridDY div b 2 div sub
rmoveto show grestore } if
/i i h add def
} repeat
grestore
} def
%
/ArcArrow {
/d ED /b ED /a ED
gsave
newpath 0 -1000 moveto clip
newpath
0 1 0 0 b
grestore
c mul
/e ED
pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul neg d
} def
%
%
/isbool { type (booleantype) cvn eq } def
%
/Ellipse {
dup isbool { /MoveToStart ED }{ /MoveToStart false def }ifelse % false or true
/rotAngle ED
/mtrx CM def
T
rotAngle rotate
scale
MoveToStart { 0 0 moveto 1 0 rmoveto } if % move to the start position
0 0 1 5 3 roll arc
mtrx setmatrix
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack: 1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
/targetLength ED /angle0 ED
/x0 rx angle0 cos mul def
/y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
targetLength 57.2958 mul
angle0 sin rx mul dup mul
angle0 cos ry mul dup mul
add sqrt div
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
dup 90 ge { pop 90 } if
angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a
% better angle (and put it on top of stack)
30 { dup
% compute distance D between (x0,y0) and M(t)
dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
exch dup cos rx mul x0 sub exch sin ry mul y0 sub
% stack contains: y(t)-y0, x(t)-x0, d
2 index Div targetLength mul y0 add ry Div exch
2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
atan exch pop
} repeat
% we don't look at what happened... in particular, if targetLength is greater
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
/d ED % is add or sub
/b ED % arrow procedure
/a1 ED % angle
gsave
newpath
0 -1000 moveto
clip % Set clippath far from arrow.
newpath
0 1 0 0 b % Draw arrow to determine length.
grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
a1 exch ArcAdjust % Angular position of base of arrow.
/a2 ED
pop pop pop
a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
a1 cos rx mul xOrig add %
a1 sin ry mul yOrig add %
% Now arrow tip coor and base coor are on stack.
b pop pop pop pop % Draw arrow, and discard coordinates.
a2 CLW 8 div
% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
ArcAdjust
% resets original value of d
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/Rot { CP CP translate 3 -1 roll neg rotate NET } def
%
/RotBegin {
tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
/TMatrix [ TMatrix CM ] cvx def
/a ED
a Rot /RAngle [ RAngle dup a add ] cvx def
} def
%
/RotEnd {
/TMatrix [ TMatrix setmatrix ] cvx def
/RAngle [ RAngle pop ] cvx def
} def
%
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/Uput {
/a ED
add 2 div /h ED 2
div /w ED
/s a sin def
/c a cos def
/b s abs c abs 2 copy gt dup
/q ED
{ pop } { exch pop } ifelse def
/w1 c b div w mul def
/h1 s b div h mul def
q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
} def
%
/UUput {
5 dict begin
/z ED
abs /y ED
/x ED
q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
{ x x mul y y mul sub z z mul add sqrt z add }
{ q { x s div } { x c div } ifelse abs
} ifelse
a PtoC
h1 add exch
w1 add exch
end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro
%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 4 2020-06-09 08:32:19Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.07, 2014/08/01
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
%currentdict /Pi known not { /Pi 3.14159265359 def } if
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
/I2P { AlgParser cvx exec } def % Infix to Postfix
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->EE
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%% NextNonBlankChar dup 0 eq { pop exit } if
%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%% AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
/NotFirst false def
{ NextNonBlankChar pop AnalyzeExpr
NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
dup Strlen eq { exit } if NextNonBlankChar
dup 44 ne 1 index 124 ne and
{ dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
if pop 1 add } loop
AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
AnalyzePreHook AnalyzeTerm IsEndingExpr
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
ifelse
AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
ifelse
AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
AnalyzePreHook 2 copy get dup IsUnaryOp
{ RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
{ pop AnalyzeFactor }
ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
AnalyzePreHook AnalyzePower IsEndingFactor
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { dup 33 eq%% is there a ! DR 09/2011
{ pop 1 add NextNonBlankChar pop EvalFactorial }
{ RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
ifelse
IsEndingFactor { pop exit } if } loop }
ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
%% depending of first char either a number, or a literal
2 copy get dup 40 eq%%an open par
{ pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
{ AnalyzeLiteral }
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
exch dup 3 -1 roll dup 3 1 roll
%%read mantissa
{ 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
dup 101 eq exch 69 eq or
%%% there is a "e" or "E" -> read exponant
{ 1 add 2 copy get dup IsUnaryOp
{ pop 1 add 2 copy get } if
{ IsNumber not { exit } if 1 add 2 copy get } loop }
if
dup 4 1 roll
3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
NextNonBlankChar 1 index 4 1 roll
{ IsCondOp not { exit } if 1 add 2 copy get } loop
2 copy 5 -1 roll
exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
dup 48 ge exch dup 57 le 3 -1 roll and exch
dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
dup 97 ge exch 122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
exch dup 3 -1 roll dup 3 1 roll
%%read literal core
{ 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
2 copy dup Strlen eq
%% if end of str is reached -> end !
{ pop pop 0 true }
%% ending chr -> clpar, comma, |, <, >, =, !,
{get dup dup 41 eq
exch dup 124 eq
exch dup 93 eq
exch dup 44 eq
exch dup 30 eq
exch dup 60 ge exch 62 le and or or or or or}
ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
/ExpressionVector ExpressionVector aload length
/fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
ReadLiteral
dup 40 eq%%% there is an open par -> function call
{ pop 2 index
dup (Sum) eq { EvalSum }
{ dup (IfTE) eq { EvalCond }
{ dup (Derive) eq { pop EvalDerive }
{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
{ /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
dup 91 eq%%% there is an open bracket -> vector element
{ pop 1 add NextNonBlankChar pop AnalyzeExpr
/ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
{ pop NextNonBlankChar pop }
ifelse}
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
%% manage the function descripiton
1 add ReadNumber 3 1 roll NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
1 add NextNonBlankChar pop
3 -1 roll cvi
dup 0 eq
{ pop AnalyzeExpr 3 -1 roll pop 1 add }
{ 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
{ (x) tx@Derive begin Derive end } repeat
ExpressionVector exch /ExpressionVector [] def
AlgToPs aload length
/ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
pop 1 add NextNonBlankChar pop
%% read the variable name
ReadLiteral pop NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
%% read the initial value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the increment value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the limit value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
/ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
5 -1 roll 4 add array astore def
%% keep ExpressionVector for later and create a new one for internal Sum computation
ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
1 add NextNonBlankChar pop AnalyzeExpr
%% add each term
/ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
/ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
dup (cos) eq 1 index (sin) eq or exch (tan) eq or
{ /ExpressionVector ExpressionVector aload length 3.1415926 /div cvx 180 /mul cvx 5 -1 roll 4 add
array astore def
} if
} def
/EvalCond {%
pop 1 add AnalyzeCond NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
ExpressionVector 3 1 roll /ExpressionVector [] def
1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
1 add AnalyzeExpr
NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
ExpressionVector
/ExpressionVector 6 -1 roll aload length dup
6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
3 -1 roll
dup (=) eq { /eq } {%
dup (<) eq { /lt } {%
dup (>) eq { /gt } {%
dup (>=) eq { /ge } {%
dup (<=) eq { /ge } {%
dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
cvx exch pop
/ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {
10240 string 3 1 roll 0 3 1 roll
/Variable exch def
tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
3 1 roll 10240 string 3 1 roll 0 3 1 roll
/Variable exch def
tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
2 copy 7 -1 roll dup length 4 1 roll putinterval add
6 -2 roll pop pop
2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
4 -2 roll 4 index (0) eq
{ (0) StrConcat 7 -1 roll pop }
{ 7 -1 roll 45 eq
{ AddSub AddOpPar true } { false } ifelse
3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
7 index dup (0) eq
{ pop true }%% du=0 nothing added
{ dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
ifelse
5 index dup (0) eq
{ pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
{ exch
{ 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
{ 5 -2 roll 7 index 43 eq%%something yet added
{ AddAdd false } { AddSub AddOpPar true } ifelse }
ifelse 11 1 roll
3 -1 roll StrConcat 10 -1 roll { AddClPar } if
2 copy pop 0 6 2 roll GetIntervalNewStr }
ifelse
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
4 -2 roll 7 index dup (0) eq
{ pop false }%%du=0
{ (1) eq%%du=1
{ false }
{ AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
true }%%du!=0
ifelse
5 1 roll 5 index (0) eq
{ 5 -1 roll not { (0) StrConcat } if }%%dv=0
{ 5 -1 roll { AddAdd } if
4 index (1) eq
{ 8 index StrConcat }
{ AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
ifelse
}%%dv!=0
ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
4 -2 roll
4 index (0) eq%%dv=0 -> u'/v
{ 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
{ 7 index dup (0) eq
{ pop }%%du=0
{ (1) eq%%du=1
{ false }
{ AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
ifelse
AddSub
4 index (1) eq
{ 8 index StrConcat }
{ AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
ifelse
%}%%dv!=0
2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
4 -2 roll 7 index (0) eq
{%%if du=0 then (u^v)'=v'ln(u)u^v
4 index (0) eq
{ (0) StrConcat }%%if dv=0 then (u^v)'=0
{ 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
}
{%%du!=0
4 index (0) eq
{%%if dv=0 then (u^v)'=vu'u^(v-1)
5 index dup IsStrNumber
{ dup (0) eq
{ StrConcat }
{ dup dup (1) eq exch (1.0) eq or
{ StrConcat }
{ StrConcat
7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
{ (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
(*\() StrConcat 8 index StrConcat (\)) StrConcat
5 index dup dup (2) eq exch (2.0) eq or
{ pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
{ pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
5 index StrConcat (-1\)) StrConcat } ifelse
}
{%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
AddOpPar 5 index StrConcat (\)*\() StrConcat
8 index StrConcat (\)^\() StrConcat
5 index StrConcat (-1\)+\() StrConcat
4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
8 index StrConcat (\)^\() StrConcat
5 index StrConcat (\)*ln\() StrConcat
8 index StrConcat AddClPar
} ifelse
} ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
4 index (0) eq
{ (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
{ DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
true exch
{ dup 48 lt exch dup 57 gt 3 -1 roll or
exch dup 46 ne%%.
exch dup 43 ne%%+
exch 45 ne%%-
and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
ReadLiteral dup 40 eq%%% there is an open par -> function call
{ pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
{ dup 91 eq%%% there is an open bracket -> vector element
{ DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
{ pop EvalVariable }
ifelse }
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
4 2 roll 4 index (1) ne
{ AddOpPar 4 index StrConcat (\)*) StrConcat } if
(Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval
/EvalFunc_sin {%
PreCommonFunc
{ (cos\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_cos {%
PreCommonFunc
{ (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_tan {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_asin {%
PreCommonFunc
{ (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_acos {%
PreCommonFunc
{ (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_atg {%
PreCommonFunc
{ (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_floor {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_ln {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_exp {%
PreCommonFunc
{ (exp\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_EXP {%
PreCommonFunc
{ (EXP\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_sqrt {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Fact {%
PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
PostCommonFunc } def
/EvalFunc_sh {%
PreCommonFunc
{ (ch\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_ch {%
PreCommonFunc
{ (sh\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_th {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argsh {%
PreCommonFunc
{ (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argch {%
PreCommonFunc
{ (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argth {%
PreCommonFunc
{ (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
4 2 roll 4 index (0) eq
{ (0) StrConcat false }
{ 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
1 add NextNonBlankChar pop
%% read the variable name
ReadLiteral pop 3 -1 roll pop NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
%% read the initial value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the increment value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
%% read the limit value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
1 add NextNonBlankChar pop dup 5 1 roll
AnalyzeExpr NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
1 add NextNonBlankChar pop
AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
dup (cos) eq 1 index (sin) eq or exch (tan) eq or
{ /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
array astore def
} if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
dup abs 1 gt { EQDFasinrangeerror } if
dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
dup abs 1 gt { EQDFacosrangeerror } if
dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro
%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.06, 2017/12/03
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
dup 0 eq { 1 }{
dup 1 gt { dup 1 sub factorial mul } if }
ifelse } def
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
2 dict begin
/n exch def /m exch def
n 0 eq { 1 }{
m n eq { 1 }{
m factorial n factorial m n sub factorial mul div } ifelse } ifelse
end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
5 dict begin % all local
aload length /n ED % number of coors
n 2 div cvi /m ED % number of Points
/n1 n def
m { n1 2 roll /n1 n1 2 sub def } repeat
n array astore
end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b]
% which is a+bi = Real+i Imag
%
/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
dup 0 get % [a1 b1] [a2 b2] a2
3 -1 roll % [a2 b2] a2 [a1 b1]
dup 0 get % [a2 b2] a2 [a1 b1] a1
3 -1 roll % [a2 b2] [a1 b1] a1 a2
add % [a2 b2] [a1 b1] a1+a2
3 1 roll % a1+a2 [a2 b2] [a1 b1]
1 get % a1+a2 [a2 b2] b1
exch 1 get % a1+a2 b1 b2
add 2 array astore
} def
%
/cxneg { % [a b]
dup 1 get % [a b] b
exch 0 get % b a
neg exch neg % -a -b
2 array astore
} def
%
/cxsub { cxneg cxadd } def % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul { % [a1 b1] [a2 b2]
dup 0 get % [a1 b1] [a2 b2] a2
exch 1 get % [a1 b1] a2 b2
3 -1 roll % a2 b2 [a1 b1]
dup 0 get % a2 b2 [a1 b1] a1
exch 1 get % a2 b2 a1 b1
dup % a2 b2 a1 b1 b1
5 -1 roll dup % b2 a1 b1 b1 a2 a2
3 1 roll mul % b2 a1 b1 a2 b1a2
5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
4 -1 roll add % b1 a2 a1 b2 b3
4 2 roll mul % b1 b2 b3 a1a2
4 2 roll mul sub % b3 a3
exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr { % [a b] square root
dup 0 get exch 1 get % a b
dup dup mul % a b b^2
3 -1 roll % b b^2 a
dup dup mul % b b^2 a a^2
3 -1 roll sub % b a a2
3 1 roll mul 2 mul % a2 b2
2 array astore
} def
%
/cxsqrt { % [a b]
% dup cxnorm sqrt /r exch def
% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
cxlog % log[a b]
2 cxrdiv % log[a b]/2
aload pop exch % b a
2.781 exch exp % b exp(a)
exch cxconv exch % [Re +iIm] exp(a)
cxrmul %
} def
%
/cxarg { % [a b]
aload pop % a b
exch atan % arctan b/a
DegtoRad % arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog { % [a b]
dup % [a b][a b]
cxnorm % [a b] |z|
log % [a b] log|z|
exch % log|z|[a b]
cxarg % log|z| Theta
cxmake2 % [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 { % [a b]
dup 0 get exch 1 get % a b
dup mul % a b^2
exch dup mul add % a^2+b^2
} def
%
/cxnorm { % [a b]
cxnorm2 sqrt
} def
%
/cxconj { % conjugent complex
dup 0 get exch 1 get % a b
neg 2 array astore % [a -b]
} def
%
/cxre { 0 get } def % real value
/cxim { 1 get } def % imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip { % [a b]
dup cxnorm2 exch % n2 [a b]
dup 0 get exch 1 get % n2 a b
3 -1 roll % a b n2
dup % a b n2 n2
4 -1 roll exch div % b n2 a/n2
3 1 roll div % a/n2 b/n2
neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul { % [a b] r
exch aload pop % r a b
3 -1 roll dup % a b r r
3 1 roll mul % a r b*r
3 1 roll mul % b*r a*r
exch 2 array astore % [a*r b*r]
} def
%
% division by a real number
/cxrdiv { % [a b] r
1 exch div % [a b] 1/r
cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv { % theta
RadtoDeg dup sin exch cos cxmake2
} def
%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
/a exch def
/n a length 1 sub def
n 0 gt {
% at this point only the n+1 items in the bottom of a remain to
% the sorted largest item in that blocks is to be moved up into
% position n
n {
0 1 n 1 sub {
/i exch def
a i get a i 1 add get gt {
% if a[i] > a[i+1] swap a[i] and a[i+1]
a i 1 add
a i get
a i a i 1 add get
% set new a[i] = old a[i+1]
put
% set new a[i+1] = old a[i]
put
} if
} for
/n n 1 sub def
} repeat
} if
a % return the sorted array
end
} def
%
/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
0 1 index { length add } forall
string
0 3 2 roll
{ 3 copy putinterval length add }forall
pop
} bind def
%
/concatstrings{ % (a) (b) -> (ab)
1 dict begin
exch dup length
2 index length add string
dup dup 4 2 roll copy length
4 -1 roll putinterval
end
} def
%
/reversestring { % (aBC) -> (CBa)
5 dict begin
/str exch def
/L str length def
/strTemp L string def
/i 0 def
L {
/I L 1 sub i sub def
strTemp i str I 1 getinterval putinterval
/i i 1 add def
} repeat
strTemp
end
} def
%
/concatarray{ % [a c] [b d] -> [a c b d]
2 dict begin
/a2 exch def
/a1 exch def
[ a1 aload pop a2 aload pop ]
end
} def
%
/dot2comma {% on stack a string (...)
2 dict begin
/Output exch def
0 1 Output length 1 sub {
/Index exch def
Output Index get 46 eq { Output Index 44 put } if
} for
Output
end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
/charNo exch def
dup
length 1 sub -1 0 {
/i exch def dup i get charNo ne { exit } if
} for
0 i 1 add getinterval
dup length string copy
} bind def % leaves the stripped string on the stack
/psStringwidth /stringwidth load def
/psShow /show load def
%/stringwidth{ 32 rightTrim psStringwidth } bind def
%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%
/pgffunctions {
/pgfsc{}bind def% stroke color is empty by default
/pgffc{}bind def% fill color is empty by default
/pgfstr{stroke}bind def%
/pgffill{fill}bind def%
/pgfeofill{eofill}bind def%
/pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
/pgfw{setlinewidth}bind def% setlinewidth
/pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
magscale{1 DVImag div dup scale}if
pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
/pgfr{pgfsd restore}bind def %restore
userdict begin%
/pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
/pgfc{newpath @endspecial pgfpd}bind def %close
/pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
/pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
/.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
/.pgfsetfillopacityalpha{/pgffoa exch def
/pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
/pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
/.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
/pgffoa 1 def
/pgfsoa 1 def
end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro
%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 4 2020-06-09 08:32:19Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02, 2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga - Dec. 16, 1999
%% Modified by Etienne Riga - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17
%
10 dict dup begin % hold local
/FontType 3 def
/FontMatrix [.001 0 0 .001 0 0] def
% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
/FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
/Encoding 256 array def
0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
Encoding % replace with given dot names
dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
% % and save /Bullet at this place in Encoding
dup (c) 0 get /Circle put
dup (C) 0 get /BoldCircle put % 67
dup (u) 0 get /SolidTriangle put
dup (t) 0 get /Triangle put
dup (T) 0 get /BoldTriangle put
dup (r) 0 get /SolidSquare put
dup (s) 0 get /Square put
dup (S) 0 get /BoldSquare put
dup (q) 0 get /SolidPentagon put
dup (p) 0 get /Pentagon put
dup (P) 0 get /BoldPentagon put
%%%
dup (k) 0 get /Asterisk put
dup (K) 0 get /BoldAsterisk put
dup (J) 0 get /SolidAsterisk put
dup (h) 0 get /Hexagon put
dup (H) 0 get /BoldHexagon put
dup (G) 0 get /SolidHexagon put
dup (f) 0 get /Octogon put % 2008-04-18 hv
dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
dup (a) 0 get /Add put
dup (A) 0 get /BoldAdd put % 65
dup (x) 0 get /Mul put
dup (X) 0 get /BoldMul put
dup (m) 0 get /Oplus put
dup (M) 0 get /BOplus put
dup (e) 0 get /SolidOplus put
dup (n) 0 get /Otimes put
dup (N) 0 get /BOtimes put
dup (E) 0 get /SolidOtimes put
dup (i) 0 get /Bar put
dup (I) 0 get /BoldBar put
dup (l) 0 get /SolidDiamond put
dup (d) 0 get /Diamond put
(D) 0 get /BoldDiamond put
%%%
/CharProcs 47 dict def
CharProcs begin
/CirclePath {0 0 500 0 360 arc closepath} def
/Bullet {CirclePath fill} def
/Circle {CirclePath .9 .9 scale CirclePath eofill} def
/BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
/TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
/SolidTriangle {TrianglePath fill} def
/Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
/BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
/SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
/SolidSquare {SquarePath fill} def
/Square {SquarePath .89 .89 scale SquarePath eofill} def
/BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
/PentagonPath {
-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
0 574.7 lineto -546.6 177.6 lineto closepath
} def
/SolidPentagon {PentagonPath fill} def
/Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
/BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
%-------------- hv begin 2004/07/25 from: er 2003/03/24
/HexagonPath {
0 550 moveto -476 275 lineto -476 -275 lineto
0 -550 lineto 476 -275 lineto 476 275 lineto closepath
} def
/SolidHexagon {HexagonPath fill} def
/Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
/BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
% 2008-04-18 hv
/OctogonPath {
550 dup 22.5 tan mul dup neg dup add /xMove exch def
exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
/SolidOctogon { OctogonPath fill } def
/Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
/BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
%
/AsteriskPath {
20 0 moveto 10 250 180 500 0 500 curveto
-180 500 -10 250 -20 0 curveto closepath
} def
/Asterisk {
AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
} def
%
/Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
/BoldAsteriskPath {
50 30 cos 100 mul moveto Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp closepath
} def
/BoldAsterisk {BoldAsteriskPath fill} def
/SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
/CrossPath {
40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
-550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
} def
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/pgf19{gsave exec 1.0 pgfw [ ] 0.0 setdash -3.00003 -5.00005 moveto
0.0 -5.00005 lineto 0.0 5.00005 lineto -3.00003 5.00005 lineto pgfstr
grestore} bind def
/pgf20{gsave exec 1.0 pgfw [ ] 0.0 setdash -2.00002 -5.00005 moveto
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bind def
/pgf21{gsave exec 1.0 pgfw [ ] 0.0 setdash -4.50003 -5.00005 moveto
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/pgf22{gsave exec 1.0 pgfw -2.50002 0.0 translate [ ] 0.0 setdash
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/pgf23{gsave exec 1.0 pgfw [ ] 0.0 setdash 1.0 0.0 moveto -5.00005
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%%BeginFont: FontAwesome5Free-Solid
%!PS-AdobeFont-1.0: FontAwesome5Free-Solid 331.008 (Font Awesome version: 5.13.0)
9 dict begin
/FontName /FontAwesome5Free-Solid def
/FontInfo 9 dict dup begin
/version (331.008 \(Font Awesome version: 5.13.0\)) readonly def
/Notice (Copyright \(c\) Font Awesome) readonly def
/FullName (Font Awesome 5 Free Solid) readonly def
/FamilyName (Font Awesome 5 Free Solid) readonly def
/Weight (Solid) readonly def
/isFixedPitch false def
/ItalicAngle 0 def
/UnderlinePosition -97.6562 def
/UnderlineThickness 48.8281 def
end readonly def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/StrokeWidth 0 def
/FontBBox {-55 -127 7797 876} readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.0: CMSY10 003.002
%%Title: CMSY10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSY10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY10 def
/FontBBox {-29 -960 1116 775 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY10.) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 2 /multiply put
dup 17 /equivalence put
dup 20 /lessequal put
dup 25 /approxequal put
dup 41 /arrowdblright put
dup 48 /prime put
dup 104 /angbracketleft put
dup 105 /angbracketright put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSSI12
%!PS-AdobeFont-1.0: CMSSI12 003.002
%%Title: CMSSI12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSSI12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSSI12 known{/CMSSI12 findfont dup/UniqueID known{dup
/UniqueID get 5000811 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSSI12 def
/FontBBox {-98 -251 1052 758 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSSI12.) readonly def
/FullName (CMSSI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 117 /u put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI10.) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 14 /delta put
dup 20 /kappa put
dup 23 /nu put
dup 27 /sigma put
dup 32 /psi put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSSI10
%!PS-AdobeFont-1.0: CMSSI10 003.002
%%Title: CMSSI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSSI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSSI10 known{/CMSSI10 findfont dup/UniqueID known{dup
/UniqueID get 5000810 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSSI10 def
/FontBBox {-97 -250 1077 759 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSSI10.) readonly def
/FullName (CMSSI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSSI9
%!PS-AdobeFont-1.0: CMSSI9 003.002
%%Title: CMSSI9
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSSI9.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSSI9 known{/CMSSI9 findfont dup/UniqueID known{dup
/UniqueID get 5000809 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSSI9 def
/FontBBox {-99 -250 1104 760 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSSI9.) readonly def
/FullName (CMSSI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 107 /k put
dup 120 /x put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMI9
%!PS-AdobeFont-1.0: CMMI9 003.002
%%Title: CMMI9
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI9.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI9 known{/CMMI9 findfont dup/UniqueID known{dup
/UniqueID get 5087384 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI9 def
/FontBBox {-29 -250 1075 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI9.) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 32 /psi put
dup 58 /period put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS9
%!PS-AdobeFont-1.0: CMSS9 003.002
%%Title: CMSS9
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS9.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSS9 known{/CMSS9 findfont dup/UniqueID known{dup
/UniqueID get 5000802 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSS9 def
/FontBBox {-63 -250 1027 760 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSS9.) readonly def
/FullName (CMSS9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 13 /fl put
dup 14 /ffi put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 51 /three put
dup 53 /five put
dup 54 /six put
dup 61 /equal put
dup 71 /G put
dup 77 /M put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.0: CMCSC10 003.002
%%Title: CMCSC10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMCSC10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup
/UniqueID get 5087402 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMCSC10 def
/FontBBox {14 -250 1077 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMCSC10.) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 58 /colon put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 73 /I put
dup 75 /K put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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%%EndFont
%%BeginFont: CMTT10
%!PS-AdobeFont-1.0: CMTT10 003.002
%%Title: CMTT10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMTT10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMTT10 known{/CMTT10 findfont dup/UniqueID known{dup
/UniqueID get 5000832 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMTT10 def
/FontBBox {-4 -233 537 696 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTT10.) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 102 /f put
dup 111 /o put
dup 114 /r put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: MSAM10
%!PS-AdobeFont-1.0: MSAM10 003.002
%%Title: MSAM10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name MSAM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSAM10 known{/MSAM10 findfont dup/UniqueID known{dup
/UniqueID get 5031981 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /MSAM10 def
/FontBBox {8 -463 1331 1003 }readonly def
/PaintType 0 def
/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name MSAM10.) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 73 /trianglerightsld put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS10
%!PS-AdobeFont-1.0: CMSS10 003.002
%%Title: CMSS10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSS10 known{/CMSS10 findfont dup/UniqueID known{dup
/UniqueID get 5000803 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSS10 def
/FontBBox {-61 -250 999 759 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSS10.) readonly def
/FullName (CMSS10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 22 /macron put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSSI8
%!PS-AdobeFont-1.0: CMSSI8 003.002
%%Title: CMSSI8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSSI8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSSI8 known{/CMSSI8 findfont dup/UniqueID known{dup
/UniqueID get 5000808 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSSI8 def
/FontBBox {-100 -250 1135 761 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSSI8.) readonly def
/FullName (CMSSI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 77 /M put
dup 83 /S put
dup 97 /a put
dup 99 /c put
dup 103 /g put
dup 106 /j put
dup 107 /k put
dup 109 /m put
dup 115 /s put
dup 116 /t put
dup 120 /x put
readonly def
currentdict end
currentfile eexec
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%%EndFont
%%BeginFont: CMMI6
%!PS-AdobeFont-1.0: CMMI6 003.002
%%Title: CMMI6
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI6.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI6 known{/CMMI6 findfont dup/UniqueID known{dup
/UniqueID get 5087381 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI6 def
/FontBBox {11 -250 1241 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI6.) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 34 /epsilon put
dup 61 /slash put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMEX10
%!PS-AdobeFont-1.0: CMEX10 003.002
%%Title: CMEX10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMEX10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup
/UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMEX10 def
/FontBBox {-24 -2960 1454 772 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMEX10.) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 32 /parenleftBigg put
dup 33 /parenrightBigg put
dup 34 /bracketleftBigg put
dup 35 /bracketrightBigg put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS8
%!PS-AdobeFont-1.0: CMSS8 003.002
%%Title: CMSS8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSS8 known{/CMSS8 findfont dup/UniqueID known{dup
/UniqueID get 5000801 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSS8 def
/FontBBox {-65 -250 1062 761 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSS8.) readonly def
/FullName (CMSS8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 1 /Delta put
dup 19 /acute put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 85 /U put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMI8
%!PS-AdobeFont-1.0: CMMI8 003.002
%%Title: CMMI8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI8 known{/CMMI8 findfont dup/UniqueID known{dup
/UniqueID get 5087383 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI8 def
/FontBBox {-24 -250 1110 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI8.) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 14 /delta put
dup 22 /mu put
dup 28 /tau put
dup 32 /psi put
dup 34 /epsilon put
dup 61 /slash put
dup 64 /partialdiff put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMI12
%!PS-AdobeFont-1.0: CMMI12 003.002
%%Title: CMMI12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI12.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI12 known{/CMMI12 findfont dup/UniqueID known{dup
/UniqueID get 5087386 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI12 def
/FontBBox {-31 -250 1026 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI12.) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 32 /psi put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSY6
%!PS-AdobeFont-1.0: CMSY6 003.002
%%Title: CMSY6
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSY6.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY6 known{/CMSY6 findfont dup/UniqueID known{dup
/UniqueID get 5096647 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY6 def
/FontBBox {-4 -948 1329 786 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY6.) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /asteriskmath put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSY8
%!PS-AdobeFont-1.0: CMSY8 003.002
%%Title: CMSY8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSY8.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY8 known{/CMSY8 findfont dup/UniqueID known{dup
/UniqueID get 5096649 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMSY8 def
/FontBBox {-30 -955 1185 779 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY8.) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /asteriskmath put
readonly def
currentdict end
currentfile eexec
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%\def\solidlineg{{\psline[linewidth=2pt,linecolor=green](0,0)(1,0)}}
%\def\dashedline{{\psline[linewidth=2pt,linecolor=red,linestyle=dashed](0,0)(1,0)}}
%\def\dashedliner{{\psline[linewidth=2pt,linecolor=red,linestyle=dashed](0,0)(1,0)}}
%\def\dashedlineg{{\psline[linewidth=2pt,linecolor=green,linestyle=dashed](0,0)(1,0)}}
%\def\dashdottedline{{\psline[linewidth=2pt,linecolor=black](0,0)(0.4,0)\psline[linewidth=2pt,linecolor=black](0.5,0)(0.6,0)\psline[linewidth=2pt,linecolor=black](0.7,0)(1.1,0)}}
%\def\dottedline{{\psline[linewidth=2pt,linecolor=red](0,0)(0.05,0)\psline[linewidth=2pt,linecolor=red](0.2,0)(0.25,0)\psline[linewidth=2pt,linecolor=red](0.4,0)(0.45,0)\psline[linewidth=2pt,linecolor=red](0.6,0)(0.65,0)}}
%
\def\solidline{\textcolor{blue}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidgreenline{\textcolor{green}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidcyanline{\textcolor{cyan}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidredline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedblackline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashdottedline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedthickline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{3pt}}%
\hspace*{0.1cm}\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{3pt}}\hspace*{0.1cm}}
\def\dottedline{\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedblackline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{2.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{2.5pt}}\hspace*{0.1cm}}
\def\uu{\langle u'u'\rangle}
\def\vv{\langle v'v'\rangle}
\def\ww{\langle w'w'\rangle}
\def\uv{\langle u'v'\rangle}
%---------------------------------------------------------------tletter
\makeatletter
\pgfarrowsdeclare{myarrow}{myarrow}{
\pgfarrowsleftextend{-5\pgflinewidth}
\pgfarrowsrightextend{5\pgflinewidth}
}
{
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\makeatother
\title[\raisebox{-0.5ex}{\psfig{figure=../brev/eps/Logotyp38mm.epsi, width=0.18\textwidth}}] % (optional, use only with long paper titles)
{ Detached Eddy Simulations: Analysis of a limit on the dissipation term for reducing spectral
energy transfer at cut-off}
\author[www.tfd.chalmers.se/\textasciitilde lada] {Lars Davidson$^*$, Christophe Friess$^{**}$}
%{}
\institute
{
$^*$Division of Fluid Dynamics\\
Dept. of Mechanics and Maritime Sciences\\
SE-412 96 Gothenburg, Sweden\\[0.3cm]
$^{**}$Aix-Marseille Universit\'e\\ CNRS, Centrale Marseille\\
M2P2 UMR 7340, 13451, Marseille, France\\[1cm]
}
\begin{document}
%-----------------------------------------------------------------------------
\begin{frame}[plain]
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{(ID)DES: physical meaning of $\psi$}
\hspace*{0.5cm}\begin{minipage}[t]{\textwidth}
\begin{eqnarray*}
C^k&= P^k + D^k - \textcolor{red}{\psi\e} & \hskip 2cm k-\text{equation} \\
C^\e&= C_{\e 1} \frac{\e}{k} P^k + D^\e - C_{\e 2} \frac{\e^2}{k} & \hskip 2cm \e-\text{equation} \\
\psi &=\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right) \nonumber
% , \quad \Delta_{max}=\max( \Delta x_1, \Delta x_2, \Delta x_3)
\end{eqnarray*}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Partition of Turbulent Kinetic Energy}
\begin{figure}
\begin{center}
\def\yy{0.}
\begin{tikzpicture}[xscale=4, yscale=4]
\draw [myarrow-myarrow] (0,1.6+\yy) -- (0,\yy) -- (2,\yy);
% kappa
\node [above right] at (2,\yy) {$\kappa$};
% E
\node [above left] at (0,1.6+\yy) {$E$};
% kappa_C
\draw [dashed,ultra thick] (1,0.2+\yy) -- (1,0.95+\yy);
\node [below] at (1,\yy) {$\kappa_c$};
\node [above] at (1,0.1+\yy) {cut-off};
% resolved
\node [above] at (0.4,0.1+\yy) {resolved};
\node [above] at (0.4,\yy) {scales};
% SGS
\node [above] at (1.5,0.1+\yy) {SGS};
\begin{axis}
[x=1cm,y=1cm,xmin=0.2,xmax=2,ymin=0.2,
axis x line=none,
axis y line=none
]
\addplot [mark=none,fill=none]file {figur/e.dat};
\end{axis}
%psi
\node at (2,1.5) {$\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$};
% eps_kappa
\draw [-myarrow] (0.95,1.1+\yy) -- (1.1,0.89+\yy);
\node [above] at (1.15,0.95+\yy) {$\e_{sgs}$};
\draw [-myarrow,red] (0.9,0.65) -- (1.1,0.65);
% delta Delta
\node [left,above] at (1.75,0.65) {$\delta \Delta_{max} < 0$};
% delta psi
\node [left,below] at (1.8,0.65) {$\delta \psi > 0$};
% delta k
\node [left,below] at (1.8,0.5) {$\delta \km < 0$};
\end{tikzpicture}
\end{center}
\caption{Energy spectrum.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Object of the Present Work}
%\stepwise{
\pause
\begin{itemize}
%\item \step{
\item To control -- limit -- how the fast energy partition (i.e. the cut-off) changes in physical space
\pause
\item i.e. limit $\dd \frac{\D \kappa_c}{\D x_j}$
\pause
\item by limiting $\dd\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right) $
\pause
\item i.e. limiting the dissipation term, $\psi\e$, in the $k$ equation
\end{itemize}
%}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis}
\pause
\begin{itemize}
\item Along mean streamlines, $\km$ and $\epm$ are assumed to be in equilibrium. We get
%
\item
\begin{eqnarray*}
\cdsdt{\km}&=& P^k + D^k - \psi \epm = 0\\
\cdsdt{\epm}&=& \cei \frac{\epm}{\km} P^k + D^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
\pause
\item For
infinitesimal perturbations we get
%
\begin{eqnarray*}
0&=& \delta P^k + \delta D^k - \epm \delta \psi \\
\label{eps-perturb-des}
0&=& \cei \frac{\epm}{\km} P^k \left( \frac{\delta P^k}{P^k} - \frac{\delta \km}{\km} \right)
+ \ceii \frac{\epm^2}{\km} \left(
\frac{\delta \km}{\km} \right) + \delta D^{\e} \\
\pause
0&=&\delta \e_M
\end{eqnarray*}
\pause
\item 5 Eqns, 7 Unknowns: $\delta \e_M$, $\delta P^k$, $\delta \psi$, $\textcolor{red}{\delta k_M}$, $\delta \e_M$,
\underline{$\delta D^k$, $\delta D^\e$}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis}
%
\pause
\begin{itemize}
\item $D^k$, $D^\e$?
%
\pause
\item Boussinesq and neglecting quadratic perturbation terms gives
\item
\pause
\begin{eqnarray*}
\underline{D^k} + \delta D^k = \frac{C_\mu}{\sigma_k} \frac{\D}{\D x_j}\left[
\underline{\frac{\km^2 } {\epm}\frac{\D\km}{\D x_j}}+
\frac{\km^2 } {\epm}\frac{\D(\delta \km)}{\D x_j}+
\frac{2(\delta \km) \km } {\epm}\frac{\D\km}{\D x_j}
\right]
\end{eqnarray*}
\end{itemize}
%
\pause
Following \cite{friess:15}, we assume that $\delta \km / \km$ does not vary in space, i.e.
%%
\pause
\begin{eqnarray*}
\frac{\D(\delta \km/\km)} {\D x_j} =0
\Rightarrow \quad
\frac{\D(\delta \km)}{\D x_j}= \frac{\delta \km}{\km} \frac{\D \km}{\D x_j}
\Rightarrow \\
%\end{eqnarray*}
%
\pause
%
%\begin{eqnarray*}
\frac{\delta D^k}{D^k} = \frac{3\delta \km}{\km} \quad \frac{\delta D^\e}{D^\e} = \frac{2\delta \km }{\km }
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis: Final Step}
%
\pause
\begin{itemize}
\item 7 Eqns, 7 Unknowns:
\pause
The perturbation analysis gives~\cite{friess-davidson:20,davidson:MoF}
%
\pause
\begin{eqnarray*}
\label{eq:dpsi}
\frac{ \delta\psi}{ \psi} &=& \frac{3\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right), \quad
\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)
\end{eqnarray*}
\pause
\item For $\psi < \ceii/\cei$: an increase in $\psi$ (a decrease in $\Delta_{max}$) $\Rightarrow$
negative $\delta \km$ (i.e. less modeled and more resolved)
\pause
\item But for $\psi > \ceii/\cei$ this relation is reversed.
\pause
\item Hence we introduce a limit: $\psi \le \ceii/\cei$ \pause $\equiv 1.9/1.5=1.27$
%
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Partition of Turbulent Kinetic Energy}
\begin{figure}
\begin{center}
\def\yy{0.}
\begin{tikzpicture}[xscale=4, yscale=4]
\draw [myarrow-myarrow] (0,1.6+\yy) -- (0,\yy) -- (2,\yy);
% kappa
\node [above right] at (2,\yy) {$\kappa$};
% E
\node [above left] at (0,1.6+\yy) {$E$};
% kappa_C
\draw [dashed,ultra thick] (1,0.2+\yy) -- (1,0.95+\yy);
\node [below] at (1,\yy) {$\kappa_c$};
\node [above] at (1,0.1+\yy) {cut-off};
% resolved
\node [above] at (0.4,0.1+\yy) {resolved};
\node [above] at (0.4,\yy) {scales};
% SGS
\node [above] at (1.5,0.1+\yy) {SGS};
\begin{axis}
[x=1cm,y=1cm,xmin=0.2,xmax=2,ymin=0.2,
axis x line=none,
axis y line=none
]
\addplot [mark=none,fill=none]file {figur/e.dat};
\end{axis}
%psi
\node at (2,1.5) {$\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$};
% eps_kappa
\draw [-myarrow] (0.95,1.1+\yy) -- (1.1,0.89+\yy);
\node [above] at (1.15,0.95+\yy) {$\e_{sgs}$};
\draw [-myarrow,red] (0.9,0.65) -- (1.1,0.65);
% delta Delta
\node [left,above] at (1.75,0.65) {$\delta \Delta_{max} < 0$};
% delta psi
\node [left,below] at (1.8,0.65) {$\delta \psi > 0$};
% delta k
\node [left,below] at (1.8,0.5) {$\delta \km < 0$};
\end{tikzpicture}
\end{center}
\caption{Energy spectrum.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis: Retaining Convection}
\pause
\begin{itemize}
\item Above we set the convection to zero, i.e.
\begin{eqnarray*}
\cdsdt{\km}&=& P^k + D^k - \psi \epm = 0\\
\cdsdt{\epm}&=& \cei \frac{\epm}{\km} P^k + D^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
%
\pause
\item Now let's keep it and neglect the diffusion ($ D^k=D^\e=0$), i.e.
\begin{eqnarray*}
P^k - C^k - \psi \epm = 0, \quad
\cei \frac{\epm}{\km} P^k - C^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
\pause
\item The perturbation analysis gives~\cite{davidson:MoF}
%
\begin{eqnarray*}
\frac{ \delta\psi}{ \psi} &= \frac{\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right) & \hskip 2cm D^k=D^\e=0\\
\pause
\frac{ \delta\psi}{ \psi} &= 3\frac{\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right) & \hskip 2cm C^k=C^\e=0
\end{eqnarray*}
%
\pause
\item Same limit: $\psi \le \ceii/\cei$
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{The Turbulence Model}
\pause
\begin{itemize}
\item The AKN low-Reynolds number of Abe \emph{et al.} ~\cite{abe:kondoh:94} is used as underlying RANS model
\begin{eqnarray*}
\label{lrn-pans-ku-eu} \frac{\D k}{\D t} + \frac{\D \ub_j k}{\D x_j} &=&
\frac{\D}{\D x_j} \left[\left(\nu + \frac{\nu_t}{\sigma_{k}}\right)\frac{\D k}{\D x_j}\right] + P_k - \textcolor{red}{\psi}\e \nonumber \\
\frac{\D \e}{\D t} + \frac{\D \ub_j \e}{\D x_j} & =& \frac{\D}{\D x_j} \left[\left(\nu +
\frac{\nu_t}{\sigma_{\e}}\right)\frac{\D \e}{\D x_j}\right] + C_{\e1}f_1 P_k\frac{\e}{k} -
C_{\e2}\frac{\e^2}{k} \nonumber\\
C_{\e1} &=& 1.5, \quad C_{\e2} = 1.9, \quad C_\mu = 0.09 \nonumber\\
\nu_t&=& C_\mu f_\mu \frac{k^2}{\e},
\quad \sigma_k = 1.4, \quad\sigma_\e = 1.4
\end{eqnarray*}
%
\pause
\item together with IDDES of Shur \emph{et. al}~\cite{shur:etal:08}
\item With $\psi \le \ceii/\cei$ is called IDDES-PC (\underline Partition \underline Control)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{The Numerical Method}
\pause
\begin{itemize}
\item The \textcolor{red}{Python} finite volume code \textcolor{red}{pyCALC-LES}~\cite{pyCALC-LES} is used.
%
\pause
\item Fully vectorized (i.e. no \texttt{for} loops).
%
\pause
\item
Fractional step. For velocities, second-order central
differencing in space and Crank-Nicolson in time.
%
\pause
\item
For $k$ and $\e$, hybrid central/upwind
scheme
\pause
\item
The discretized equations are solved with \textcolor{red}{Python sparse matrix solvers}.
\pause
\item
The \textcolor{red}{pyAMG} solver~\cite{pyamg} is used for the pressure Poisson equation (very efficient)
\pause
%\item My history of written in-house CFD codes:
%\begin{enumerate}
%\pause
%\item \textcolor{red}{TEACH3D}, RANS, SIMPLE, Cartesian/Polar, Fort77 (1986 )
%\pause
%\item \textcolor{red}{FLUX2d}, RANS, SIMPLE, curvi-linear, staggered, Fort77, 1988
%\pause
%\item \textcolor{red}{CALC-BFC}, RANS, SIMPLE, curvi-lin. coll., Fort77 (1989)
%\pause
%\item \textcolor{red}{CALC-LES}, LES and DES, fractional step, curvi-linear collocated, Fort77 (1995)
%\pause
%\item \textcolor{red}{pyCALC-LES}, LES and DES, fractional step, curvi-linear collocated, Python (2021)
%\pause
%\item \textcolor{red}{pyCALC-LES} on GPU (2022)
%\end{enumerate}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}%[allowframebreaks,allowdisplaybreaks]
\frametitle{Channel flow, periodic b.c.}
\begin{itemize}
\item $Re_\tau=u_\tau h/\nu = 5\, 200$
\item The mesh has $32\times 96 \times 32$ ($x$, $y$, $z$) cells $\Rightarrow$
$(\Delta x^+,\Delta z^+)=(800,400)$.
\end{itemize}
\pause
\begin{figure}
\hspace*{-1.3cm}
\centering
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u_log_5200-etmm13-iddes-psi-limit-fk-0.eps}
\caption{Mean velocity.}
\label{channel-u}
\end{subfigure}%
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/fk_5200-etmm13-iddes-psi-limit-fk-0.eps}
\caption{$\psi$}
\label{channel-fk}
\end{subfigure}%
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/vis_5200-no-smag-etmm13-iddes-psi-limit-fk-0.eps}
\caption{Turbulent viscosity}
\label{channel-vis}
\end{subfigure}
\caption{
\solidline: IDDES-PC model; \dashedline: IDDES; Markers: ~DNS~\cite{moser:15}}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Channel flow inlet-outlet}
\begin{itemize}
\item RANS inlet values on $k$ and $\e$.
\end{itemize}
\pause
\begin{figure}
\hspace*{-1.0cm}
\centering
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.7cm,clip=]{figur/k_python-5200-inlet-etmm13-iddes.eps}
\caption{Modeled $k$.}
\label{channel-inlet-k}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.9cm,clip=]{figur/fk_python-5200-inlet-etmm13-iddes.eps}
\caption{$\psi$.}
\label{fk-inlet-k}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.9cm,clip=]{figur/vis_python-5200-inlet-etmm13-iddes.eps}
\caption{Turbulent viscosity.}
\label{channel-inlet-vis}
\end{subfigure}%
\caption{Profiles at $x=\delta$, i.e. one half-channel width.}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow}
\begin{itemize}
\item The Reynolds number is $Re_c=936\, 000$
\item The spanwise extent is $z_{max}=0.2$.
\item The mesh has $582 \times 128 \times 32$ cells ($x$, $y$, $z$)
\end{itemize}
\pause
\begin{figure}
\hspace*{-2cm}
\centering
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.6cm,clip=]{figur/grid_etmm13-pitm.eps}
\caption{Grid.}
\label{hump-grid}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.3cm,clip=]{figur/cp_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Pressure coefficient.}
\label{hump-cp}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.3cm,clip=]{figur/cf_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Skin friction}
\label{hump-cf}
\end{subfigure}%
\caption{\solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\label{hump-cp-cf}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Velocities.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u065_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=0.65$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u100_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.0$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u130_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.30$.}
\end{subfigure}
\caption{ \solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Shear stresses.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv065_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=0.65$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv100_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.0$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv130_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.30$.}
\end{subfigure}
\caption{ \solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\end{figure}
\end{frame}
%\begin{frame} % [allowframebreaks,allowdisplaybreaks]
%\frametitle{hump flow. $\psi$.}
%
%\begin{figure}
%\hspace*{-1cm}
%\captionsetup[subfigure]{justification=centering}
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk065-dt-0.003-7500.eps}
%\caption{$x=0.65$.}
%\end{subfigure}%
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk100-dt-0.003-7500.eps}
%\caption{$x=1.0$.}
%\end{subfigure}%
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk130-dt-0.003-7500.eps}
%\caption{$x=1.30$.}
%\end{subfigure}
%\vspace*{-0.3cm}
%\caption{ \solidline: IDDES-PC model; \dashedline. IDDES.}
%\end{figure}
%
%\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Turbulent Viscosity and $\langle u'u'\rangle$.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.6cm,clip=]{figur/grid_etmm13-pitm.eps}
\caption{Grid.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uu000_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Streamwise fluctuations.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/vis065_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Turbulent viscosity.}
\end{subfigure}%
\caption{$x=0$. \solidline: IDDES-PC model; \dashedline. IDDES.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Conclusions}
\begin{itemize}
\item A limiter on $\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$ is proposed which reads
\pause
\item $\psi \le \ceii/\cei$ \pause $\equiv 1.9/1.5=1.27$
\pause
\item The limiter is derived using perturbation analysis which assumes
\begin{eqnarray*}
\frac{\D(\delta \km)}{\D x_j}= \frac{\delta \km}{\km} \frac{\D \km}{\D x_j}
\end{eqnarray*}
\pause
%
\item The limiter is shown to reduce $\frac{\D(\delta \km)}{\D x_j}$
\pause
\item Good results are obtained (better than standard IDDES for the hump flow)
\end{itemize}
\end{frame}
%
\begin{frame}[allowframebreaks,allowdisplaybreaks]
\frametitle{References}
% show numbers on references
\usebibitemtemplate{\insertbiblabel}\usebibitemtemplate{\insertbiblabel}
%\bibliographystyle{plainnat}
\bibliography{../bibfil}
\end{frame}
\end{document}
latex_slides_beamer_example/slides.toc 0000664 0001750 0001750 00000000000 14155066220 017133 0 ustar lada lada latex_slides_beamer_example/slides.bbl 0000664 0001750 0001750 00000005023 14155066205 017122 0 ustar lada lada \begin{thebibliography}{10}
\bibitem{abe:kondoh:94}
K.~Abe, T.~Kondoh, and Y.~Nagano.
\newblock A new turbulence model for predicting fluid flow and heat transfer in
separating and reattaching flows - 1. {F}low field calculations.
\newblock {\em Int. J. Heat Mass Transfer}, 37(1):139--151, 1994.
\bibitem{davidson:MoF}
L.~Davidson.
\newblock Fluid mechanics, turbulent flow and turbulence
modeling\href{http://www.tfd.chalmers.se/~lada/postscript_files/solids-and-fluids\_turbulent-flow_turbulence-modelling.pdf}{\faIcon{external-link-alt}}.
\newblock eBook, Division of Fluid Dynamics, Dept. of Mechanics and Maritime
Sciences, Chalmers University of Technology{,} Gothenburg, 2021.
\bibitem{pyCALC-LES}
L.~Davidson.
\newblock {pyCALC-LES:} a {P}ython code for {DNS}, {LES} and {H}ybrid
{LES-RANS}\href{http://www.tfd.chalmers.se/~lada/postscript_files/py-calc-les.pdf}{\faIcon{external-link-alt}}.
\newblock Division of Fluid Dynamics, Dept. of Mechanics and Maritime Sciences,
Chalmers University of Technology{,} Gothenburg, 2021.
\bibitem{friess-davidson:20}
C.~Friess and L.~Davidson.
\newblock A formulation of {PANS} able to mimic {IDDES}.
\newblock {\em International Journal of Heat and Fluid Flow}, 86(108666), 2020.
\bibitem{friess:15}
C.~Friess, R.~Manceau, and T.B. Gatski.
\newblock Toward an equivalence criterion for hybrid {RANS/LES} methods.
\newblock {\em International Journal of Heat and Fluid Flow}, 122:233--246,
2015.
\bibitem{greenblatt:05}
D.~Greenblatt, K.~B. Paschal, C.-S. Yao, and J.~Harris.
\newblock A separation control {CFD} validation test case {P}art 1: Zero efflux
oscillatory blowing.
\newblock AIAA-2005-0485, 2005.
\bibitem{greenblatt:04}
D.~Greenblatt, K.~B. Paschal, C.-S. Yao, J.~Harris, N.~W. Schaeffler, and A.~E.
Washburn.
\newblock A separation control {CFD} validation test case. {P}art 1: Baseline
\& steady suction.
\newblock AIAA-2004-2220, 2004.
\bibitem{moser:15}
M.~Lee and R.~D. Moser.
\newblock Direct numerical simulation of turbulent channel flow up to
$\mathit{Re}_{{\it\tau}}\approx 5200$.
\newblock {\em Journal of Fluid Mechanics}, 774:395--415, 2015.
\bibitem{pyamg}
L.~N. Olson and J.~B. Schroder.
\newblock {PyAMG}: Algebraic multigrid solvers in {Python} v4.0, 2018.
\newblock Release 4.0.
\bibitem{shur:etal:08}
M.~L. Shur, P.~R. Spalart, M.~Kh. Strelets, and A.~K. Travin.
\newblock A hybrid {RANS-LES} approach with delayed-{DES} and wall-modelled
{LES} capabilities.
\newblock {\em International Journal of Heat and Fluid Flow}, 29:1638--1649,
2008.
\end{thebibliography}
latex_slides_beamer_example/slides.blg 0000664 0001750 0001750 00000001576 14155066205 017140 0 ustar lada lada This is BibTeX, Version 0.99d (TeX Live 2020/Debian)
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latex_slides_beamer_example/slides.tex 0000640 0001750 0001750 00000055431 14155066175 017173 0 ustar lada lada \PassOptionsToPackage{usenames,dvipsnames}{xcolor}
%\documentclass[hyperref={colorlinks = true,linkcolor = blue}]{beamer}
\documentclass[hyperref={colorlinks=true,linkcolor=blue,anchorcolor=blue,urlcolor=blue,citecolor=blue,breaklinks=true}]{beamer}
%\documentclass{beamer}
\usetheme{default} %bäst
\def\redtri{\textcolor{red}{$\blacktriangleright$}}
\usefonttheme[onlylarge]{structuresmallcapsserif}
%\usepackage[square,numbers]{natbib}
\usepackage{natbib}
%\bibliographystyle{unsrtnat}
\bibliographystyle{plain}
\usepackage[utf8]{inputenc}
\usepackage[export]{adjustbox}
\usepackage[compatibility=false]{caption}
\usepackage{subcaption}
\usepackage[display]{texpower}
%\usepackage{texpower} % printout
%---------------------------------------------------------------
%\usepackage{url}
\usepackage{tikz,xifthen,pgfplots}
\usepackage{pstricks}
\usepackage{epsfig}
\usepackage{psfrag}
\def\karm{von K\'arm\'an }
%\usepackage{hyperref}
%\usepackage[colorlinks=true,linkcolor=blue,anchorcolor=blue,urlcolor=blue,citecolor=blue,breaklinks=true]{hyperref}
\usepackage{fontawesome5}
\usepackage{breakurl}
\def\km{k_M}
\def\epm{\e_M}
\newcommand{\cdsdt}[1]{\displaystyle\frac{d #1}{d t}}
\newcommand{\cei}{C_{\e 1}}
\newcommand{\ceii}{C_{\e 2}}
\newcommand{\ceiis}{C^*_{\e 2}}
\def\e{\varepsilon}
\def\uij{\langle u'_iu'_j\rangle}
\def\dd{\displaystyle}
\def\tb{{\bar{t}}}
\def\ub{{\bar{u}}}
\def\vb{{\bar{v}}}
\def\wb{{\bar{w}}}
\def\pb{{\bar{p}}}
\def\sb{{\bar{s}}}
\def\dprime{^{\prime\prime}}
\def\redbullet{{\color{red}$\bullet$ }}
\def\wt{\overline{w't'}}
\def\uw{\overline{u'w'}}
\def\D{\partial}
%\def\solidline{{\psline[linewidth=2pt,linecolor=blue](0,0)(1,0)}}
%\def\solidlineg{{\psline[linewidth=2pt,linecolor=green](0,0)(1,0)}}
%\def\dashedline{{\psline[linewidth=2pt,linecolor=red,linestyle=dashed](0,0)(1,0)}}
%\def\dashedliner{{\psline[linewidth=2pt,linecolor=red,linestyle=dashed](0,0)(1,0)}}
%\def\dashedlineg{{\psline[linewidth=2pt,linecolor=green,linestyle=dashed](0,0)(1,0)}}
%\def\dashdottedline{{\psline[linewidth=2pt,linecolor=black](0,0)(0.4,0)\psline[linewidth=2pt,linecolor=black](0.5,0)(0.6,0)\psline[linewidth=2pt,linecolor=black](0.7,0)(1.1,0)}}
%\def\dottedline{{\psline[linewidth=2pt,linecolor=red](0,0)(0.05,0)\psline[linewidth=2pt,linecolor=red](0.2,0)(0.25,0)\psline[linewidth=2pt,linecolor=red](0.4,0)(0.45,0)\psline[linewidth=2pt,linecolor=red](0.6,0)(0.65,0)}}
%
\def\solidline{\textcolor{blue}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidgreenline{\textcolor{green}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidcyanline{\textcolor{cyan}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\solidredline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.6cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedblackline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashdottedline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedthickline{\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{3pt}}%
\hspace*{0.1cm}\textcolor{red}{\protect\rule[0.15\baselineskip]{0.2cm}{3pt}}\hspace*{0.1cm}}
\def\dottedline{\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}%
\hspace*{0.1cm}\textcolor{green}{\protect\rule[0.15\baselineskip]{0.05cm}{1.5pt}}\hspace*{0.1cm}}
\def\dashedblackline{\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{2.5pt}}%
\hspace*{0.1cm}\textcolor{black}{\protect\rule[0.15\baselineskip]{0.2cm}{2.5pt}}\hspace*{0.1cm}}
\def\uu{\langle u'u'\rangle}
\def\vv{\langle v'v'\rangle}
\def\ww{\langle w'w'\rangle}
\def\uv{\langle u'v'\rangle}
%---------------------------------------------------------------tletter
\makeatletter
\pgfarrowsdeclare{myarrow}{myarrow}{
\pgfarrowsleftextend{-5\pgflinewidth}
\pgfarrowsrightextend{5\pgflinewidth}
}
{
\newlength\pgf@my@length
\pgf@my@length = 1cm
\divide \pgf@my@length by 16
\pgfpathmoveto{\pgfpoint{-.7\pgf@my@length}{0pt}}
\pgfpathlineto{\pgfpoint{-.7\pgf@my@length}{-.8\pgf@my@length}}
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\pgfpathlineto{\pgfpoint{-.7\pgf@my@length}{.8\pgf@my@length}}
\pgfpathlineto{\pgfpoint{-.7\pgf@my@length}{0pt}}
\pgfusepathqfillstroke
}
\makeatother
\title[\raisebox{-0.5ex}{\psfig{figure=../brev/eps/Logotyp38mm.epsi, width=0.18\textwidth}}] % (optional, use only with long paper titles)
{ Detached Eddy Simulations: Analysis of a limit on the dissipation term for reducing spectral
energy transfer at cut-off}
\author[www.tfd.chalmers.se/\textasciitilde lada] {Lars Davidson$^*$, Christophe Friess$^{**}$}
%{}
\institute
{
$^*$Division of Fluid Dynamics\\
Dept. of Mechanics and Maritime Sciences\\
SE-412 96 Gothenburg, Sweden\\[0.3cm]
$^{**}$Aix-Marseille Universit\'e\\ CNRS, Centrale Marseille\\
M2P2 UMR 7340, 13451, Marseille, France\\[1cm]
}
\begin{document}
%-----------------------------------------------------------------------------
\begin{frame}[plain]
\titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{(ID)DES: physical meaning of $\psi$}
\hspace*{0.5cm}\begin{minipage}[t]{\textwidth}
\begin{eqnarray*}
C^k&= P^k + D^k - \textcolor{red}{\psi\e} & \hskip 2cm k-\text{equation} \\
C^\e&= C_{\e 1} \frac{\e}{k} P^k + D^\e - C_{\e 2} \frac{\e^2}{k} & \hskip 2cm \e-\text{equation} \\
\psi &=\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right) \nonumber
% , \quad \Delta_{max}=\max( \Delta x_1, \Delta x_2, \Delta x_3)
\end{eqnarray*}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Partition of Turbulent Kinetic Energy}
\begin{figure}
\begin{center}
\def\yy{0.}
\begin{tikzpicture}[xscale=4, yscale=4]
\draw [myarrow-myarrow] (0,1.6+\yy) -- (0,\yy) -- (2,\yy);
% kappa
\node [above right] at (2,\yy) {$\kappa$};
% E
\node [above left] at (0,1.6+\yy) {$E$};
% kappa_C
\draw [dashed,ultra thick] (1,0.2+\yy) -- (1,0.95+\yy);
\node [below] at (1,\yy) {$\kappa_c$};
\node [above] at (1,0.1+\yy) {cut-off};
% resolved
\node [above] at (0.4,0.1+\yy) {resolved};
\node [above] at (0.4,\yy) {scales};
% SGS
\node [above] at (1.5,0.1+\yy) {SGS};
\begin{axis}
[x=1cm,y=1cm,xmin=0.2,xmax=2,ymin=0.2,
axis x line=none,
axis y line=none
]
\addplot [mark=none,fill=none]file {figur/e.dat};
\end{axis}
%psi
\node at (2,1.5) {$\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$};
% eps_kappa
\draw [-myarrow] (0.95,1.1+\yy) -- (1.1,0.89+\yy);
\node [above] at (1.15,0.95+\yy) {$\e_{sgs}$};
\draw [-myarrow,red] (0.9,0.65) -- (1.1,0.65);
% delta Delta
\node [left,above] at (1.75,0.65) {$\delta \Delta_{max} < 0$};
% delta psi
\node [left,below] at (1.8,0.65) {$\delta \psi > 0$};
% delta k
\node [left,below] at (1.8,0.5) {$\delta \km < 0$};
\end{tikzpicture}
\end{center}
\caption{Energy spectrum.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Object of the Present Work}
%\stepwise{
\pause
\begin{itemize}
%\item \step{
\item To control -- limit -- how the fast energy partition (i.e. the cut-off) changes in physical space
\pause
\item i.e. limit $\dd \frac{\D \kappa_c}{\D x_j}$
\pause
\item by limiting $\dd\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right) $
\pause
\item i.e. limiting the dissipation term, $\psi\e$, in the $k$ equation
\end{itemize}
%}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis}
\pause
\begin{itemize}
\item Along mean streamlines, $\km$ and $\epm$ are assumed to be in equilibrium. We get
%
\item
\begin{eqnarray*}
\cdsdt{\km}&=& P^k + D^k - \psi \epm = 0\\
\cdsdt{\epm}&=& \cei \frac{\epm}{\km} P^k + D^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
\pause
\item For
infinitesimal perturbations we get
%
\begin{eqnarray*}
0&=& \delta P^k + \delta D^k - \epm \delta \psi \\
\label{eps-perturb-des}
0&=& \cei \frac{\epm}{\km} P^k \left( \frac{\delta P^k}{P^k} - \frac{\delta \km}{\km} \right)
+ \ceii \frac{\epm^2}{\km} \left(
\frac{\delta \km}{\km} \right) + \delta D^{\e} \\
\pause
0&=&\delta \e_M
\end{eqnarray*}
\pause
\item 5 Eqns, 7 Unknowns: $\delta \e_M$, $\delta P^k$, $\delta \psi$, $\textcolor{red}{\delta k_M}$, $\delta \e_M$,
\underline{$\delta D^k$, $\delta D^\e$}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis}
%
\pause
\begin{itemize}
\item $D^k$, $D^\e$?
%
\pause
\item Boussinesq and neglecting quadratic perturbation terms gives
\item
\pause
\begin{eqnarray*}
\underline{D^k} + \delta D^k = \frac{C_\mu}{\sigma_k} \frac{\D}{\D x_j}\left[
\underline{\frac{\km^2 } {\epm}\frac{\D\km}{\D x_j}}+
\frac{\km^2 } {\epm}\frac{\D(\delta \km)}{\D x_j}+
\frac{2(\delta \km) \km } {\epm}\frac{\D\km}{\D x_j}
\right]
\end{eqnarray*}
\end{itemize}
%
\pause
Following \cite{friess:15}, we assume that $\delta \km / \km$ does not vary in space, i.e.
%%
\pause
\begin{eqnarray*}
\frac{\D(\delta \km/\km)} {\D x_j} =0
\Rightarrow \quad
\frac{\D(\delta \km)}{\D x_j}= \frac{\delta \km}{\km} \frac{\D \km}{\D x_j}
\Rightarrow \\
%\end{eqnarray*}
%
\pause
%
%\begin{eqnarray*}
\frac{\delta D^k}{D^k} = \frac{3\delta \km}{\km} \quad \frac{\delta D^\e}{D^\e} = \frac{2\delta \km }{\km }
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis: Final Step}
%
\pause
\begin{itemize}
\item 7 Eqns, 7 Unknowns:
\pause
The perturbation analysis gives~\cite{friess-davidson:20,davidson:MoF}
%
\pause
\begin{eqnarray*}
\label{eq:dpsi}
\frac{ \delta\psi}{ \psi} &=& \frac{3\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right), \quad
\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)
\end{eqnarray*}
\pause
\item For $\psi < \ceii/\cei$: an increase in $\psi$ (a decrease in $\Delta_{max}$) $\Rightarrow$
negative $\delta \km$ (i.e. less modeled and more resolved)
\pause
\item But for $\psi > \ceii/\cei$ this relation is reversed.
\pause
\item Hence we introduce a limit: $\psi \le \ceii/\cei$ \pause $\equiv 1.9/1.5=1.27$
%
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Partition of Turbulent Kinetic Energy}
\begin{figure}
\begin{center}
\def\yy{0.}
\begin{tikzpicture}[xscale=4, yscale=4]
\draw [myarrow-myarrow] (0,1.6+\yy) -- (0,\yy) -- (2,\yy);
% kappa
\node [above right] at (2,\yy) {$\kappa$};
% E
\node [above left] at (0,1.6+\yy) {$E$};
% kappa_C
\draw [dashed,ultra thick] (1,0.2+\yy) -- (1,0.95+\yy);
\node [below] at (1,\yy) {$\kappa_c$};
\node [above] at (1,0.1+\yy) {cut-off};
% resolved
\node [above] at (0.4,0.1+\yy) {resolved};
\node [above] at (0.4,\yy) {scales};
% SGS
\node [above] at (1.5,0.1+\yy) {SGS};
\begin{axis}
[x=1cm,y=1cm,xmin=0.2,xmax=2,ymin=0.2,
axis x line=none,
axis y line=none
]
\addplot [mark=none,fill=none]file {figur/e.dat};
\end{axis}
%psi
\node at (2,1.5) {$\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$};
% eps_kappa
\draw [-myarrow] (0.95,1.1+\yy) -- (1.1,0.89+\yy);
\node [above] at (1.15,0.95+\yy) {$\e_{sgs}$};
\draw [-myarrow,red] (0.9,0.65) -- (1.1,0.65);
% delta Delta
\node [left,above] at (1.75,0.65) {$\delta \Delta_{max} < 0$};
% delta psi
\node [left,below] at (1.8,0.65) {$\delta \psi > 0$};
% delta k
\node [left,below] at (1.8,0.5) {$\delta \km < 0$};
\end{tikzpicture}
\end{center}
\caption{Energy spectrum.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Perturbation Analysis: Retaining Convection}
\pause
\begin{itemize}
\item Above we set the convection to zero, i.e.
\begin{eqnarray*}
\cdsdt{\km}&=& P^k + D^k - \psi \epm = 0\\
\cdsdt{\epm}&=& \cei \frac{\epm}{\km} P^k + D^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
%
\pause
\item Now let's keep it and neglect the diffusion ($ D^k=D^\e=0$), i.e.
\begin{eqnarray*}
P^k - C^k - \psi \epm = 0, \quad
\cei \frac{\epm}{\km} P^k - C^{\e} - \ceii \frac{\epm^2}{\km} = 0
\end{eqnarray*}
\pause
\item The perturbation analysis gives~\cite{davidson:MoF}
%
\begin{eqnarray*}
\frac{ \delta\psi}{ \psi} &= \frac{\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right) & \hskip 2cm D^k=D^\e=0\\
\pause
\frac{ \delta\psi}{ \psi} &= 3\frac{\delta \km}{\km}\left( 1 - \frac{ \ceii}{\cei\psi}\right) & \hskip 2cm C^k=C^\e=0
\end{eqnarray*}
%
\pause
\item Same limit: $\psi \le \ceii/\cei$
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{The Turbulence Model}
\pause
\begin{itemize}
\item The AKN low-Reynolds number of Abe \emph{et al.} ~\cite{abe:kondoh:94} is used as underlying RANS model
\begin{eqnarray*}
\label{lrn-pans-ku-eu} \frac{\D k}{\D t} + \frac{\D \ub_j k}{\D x_j} &=&
\frac{\D}{\D x_j} \left[\left(\nu + \frac{\nu_t}{\sigma_{k}}\right)\frac{\D k}{\D x_j}\right] + P_k - \textcolor{red}{\psi}\e \nonumber \\
\frac{\D \e}{\D t} + \frac{\D \ub_j \e}{\D x_j} & =& \frac{\D}{\D x_j} \left[\left(\nu +
\frac{\nu_t}{\sigma_{\e}}\right)\frac{\D \e}{\D x_j}\right] + C_{\e1}f_1 P_k\frac{\e}{k} -
C_{\e2}\frac{\e^2}{k} \nonumber\\
C_{\e1} &=& 1.5, \quad C_{\e2} = 1.9, \quad C_\mu = 0.09 \nonumber\\
\nu_t&=& C_\mu f_\mu \frac{k^2}{\e},
\quad \sigma_k = 1.4, \quad\sigma_\e = 1.4
\end{eqnarray*}
%
\pause
\item together with IDDES of Shur \emph{et. al}~\cite{shur:etal:08}
\item With $\psi \le \ceii/\cei$ is called IDDES-PC (\underline Partition \underline Control)
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{The Numerical Method}
\pause
\begin{itemize}
\item The \textcolor{red}{Python} finite volume code \textcolor{red}{pyCALC-LES}~\cite{pyCALC-LES} is used.
%
\pause
\item Fully vectorized (i.e. no \texttt{for} loops).
%
\pause
\item
Fractional step. For velocities, second-order central
differencing in space and Crank-Nicolson in time.
%
\pause
\item
For $k$ and $\e$, hybrid central/upwind
scheme
\pause
\item
The discretized equations are solved with \textcolor{red}{Python sparse matrix solvers}.
\pause
\item
The \textcolor{red}{pyAMG} solver~\cite{pyamg} is used for the pressure Poisson equation (very efficient)
\pause
%\item My history of written in-house CFD codes:
%\begin{enumerate}
%\pause
%\item \textcolor{red}{TEACH3D}, RANS, SIMPLE, Cartesian/Polar, Fort77 (1986 )
%\pause
%\item \textcolor{red}{FLUX2d}, RANS, SIMPLE, curvi-linear, staggered, Fort77, 1988
%\pause
%\item \textcolor{red}{CALC-BFC}, RANS, SIMPLE, curvi-lin. coll., Fort77 (1989)
%\pause
%\item \textcolor{red}{CALC-LES}, LES and DES, fractional step, curvi-linear collocated, Fort77 (1995)
%\pause
%\item \textcolor{red}{pyCALC-LES}, LES and DES, fractional step, curvi-linear collocated, Python (2021)
%\pause
%\item \textcolor{red}{pyCALC-LES} on GPU (2022)
%\end{enumerate}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}%[allowframebreaks,allowdisplaybreaks]
\frametitle{Channel flow, periodic b.c.}
\begin{itemize}
\item $Re_\tau=u_\tau h/\nu = 5\, 200$
\item The mesh has $32\times 96 \times 32$ ($x$, $y$, $z$) cells $\Rightarrow$
$(\Delta x^+,\Delta z^+)=(800,400)$.
\end{itemize}
\pause
\begin{figure}
\hspace*{-1.3cm}
\centering
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u_log_5200-etmm13-iddes-psi-limit-fk-0.eps}
\caption{Mean velocity.}
\label{channel-u}
\end{subfigure}%
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/fk_5200-etmm13-iddes-psi-limit-fk-0.eps}
\caption{$\psi$}
\label{channel-fk}
\end{subfigure}%
\begin{subfigure}[t]{0.40\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/vis_5200-no-smag-etmm13-iddes-psi-limit-fk-0.eps}
\caption{Turbulent viscosity}
\label{channel-vis}
\end{subfigure}
\caption{
\solidline: IDDES-PC model; \dashedline: IDDES; Markers: ~DNS~\cite{moser:15}}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Channel flow inlet-outlet}
\begin{itemize}
\item RANS inlet values on $k$ and $\e$.
\end{itemize}
\pause
\begin{figure}
\hspace*{-1.0cm}
\centering
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.7cm,clip=]{figur/k_python-5200-inlet-etmm13-iddes.eps}
\caption{Modeled $k$.}
\label{channel-inlet-k}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.9cm,clip=]{figur/fk_python-5200-inlet-etmm13-iddes.eps}
\caption{$\psi$.}
\label{fk-inlet-k}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=3.9cm,clip=]{figur/vis_python-5200-inlet-etmm13-iddes.eps}
\caption{Turbulent viscosity.}
\label{channel-inlet-vis}
\end{subfigure}%
\caption{Profiles at $x=\delta$, i.e. one half-channel width.}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow}
\begin{itemize}
\item The Reynolds number is $Re_c=936\, 000$
\item The spanwise extent is $z_{max}=0.2$.
\item The mesh has $582 \times 128 \times 32$ cells ($x$, $y$, $z$)
\end{itemize}
\pause
\begin{figure}
\hspace*{-2cm}
\centering
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.6cm,clip=]{figur/grid_etmm13-pitm.eps}
\caption{Grid.}
\label{hump-grid}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.3cm,clip=]{figur/cp_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Pressure coefficient.}
\label{hump-cp}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.3cm,clip=]{figur/cf_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Skin friction}
\label{hump-cf}
\end{subfigure}%
\caption{\solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\label{hump-cp-cf}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Velocities.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u065_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=0.65$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u100_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.0$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/u130_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.30$.}
\end{subfigure}
\caption{ \solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\end{figure}
\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Shear stresses.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv065_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=0.65$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv100_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.0$.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uv130_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{$x=1.30$.}
\end{subfigure}
\caption{ \solidline: IDDES-PC model; \dashedline. IDDES. Markers: experiments~\cite{greenblatt:04,greenblatt:05}}
\end{figure}
\end{frame}
%\begin{frame} % [allowframebreaks,allowdisplaybreaks]
%\frametitle{hump flow. $\psi$.}
%
%\begin{figure}
%\hspace*{-1cm}
%\captionsetup[subfigure]{justification=centering}
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk065-dt-0.003-7500.eps}
%\caption{$x=0.65$.}
%\end{subfigure}%
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk100-dt-0.003-7500.eps}
%\caption{$x=1.0$.}
%\end{subfigure}%
%\begin{subfigure}[t]{0.4\textwidth}
%\centering
%\includegraphics[width=4.0cm,clip=]{../etmm13-pitm/figur/fk130-dt-0.003-7500.eps}
%\caption{$x=1.30$.}
%\end{subfigure}
%\vspace*{-0.3cm}
%\caption{ \solidline: IDDES-PC model; \dashedline. IDDES.}
%\end{figure}
%
%\end{frame}
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{hump flow. Turbulent Viscosity and $\langle u'u'\rangle$.}
\begin{figure}
\hspace*{-1cm}
\captionsetup[subfigure]{justification=centering}
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.6cm,clip=]{figur/grid_etmm13-pitm.eps}
\caption{Grid.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/uu000_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Streamwise fluctuations.}
\end{subfigure}%
\begin{subfigure}[t]{0.4\textwidth}
\centering
\includegraphics[width=4.0cm,clip=]{figur/vis065_hump_etmm13-pitm-fk-0-ne-0-dt-0.003-7500.eps}
\caption{Turbulent viscosity.}
\end{subfigure}%
\caption{$x=0$. \solidline: IDDES-PC model; \dashedline. IDDES.}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} % [allowframebreaks,allowdisplaybreaks]
\frametitle{Conclusions}
\begin{itemize}
\item A limiter on $\psi =\max\left(1,\frac{k^{3/2}/\e}{C_{DES} \Delta_{max}}\right)$ is proposed which reads
\pause
\item $\psi \le \ceii/\cei$ \pause $\equiv 1.9/1.5=1.27$
\pause
\item The limiter is derived using perturbation analysis which assumes
\begin{eqnarray*}
\frac{\D(\delta \km)}{\D x_j}= \frac{\delta \km}{\km} \frac{\D \km}{\D x_j}
\end{eqnarray*}
\pause
%
\item The limiter is shown to reduce $\frac{\D(\delta \km)}{\D x_j}$
\pause
\item Good results are obtained (better than standard IDDES for the hump flow)
\end{itemize}
\end{frame}
%
\begin{frame}[allowframebreaks,allowdisplaybreaks]
\frametitle{References}
% show numbers on references
\usebibitemtemplate{\insertbiblabel}\usebibitemtemplate{\insertbiblabel}
%\bibliographystyle{plainnat}
\bibliography{bibfil}
\end{frame}
\end{document}
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