development of one-equation subgrid models

Researcher: Lars Davidson
Supervisor: -
Cooperation: -
Sponsors: -
Publications: [1-12], see references below
Start of project: spring 1996

The standard dynamic subgrid model (the Germano model) has numerical stability problems. The remedy is to average in some homogeneous flow direction(s) or to introduce some artificial clipping. Thus this type of models does not seem to be applicable to real three-dimensional flow without introducing ad hoc user modifications.
In the present study a new one-equation subgrid model is presented which eliminates the need of this type of user modification. The idea is to include all local dynamic information into the source terms of the transport equation of ksgs. In this way the numerical algorithm can accept local, wildly fluctuating dynamic coefficients. Negative values of the dynamic coefficient in the production term are permitted, thus allowing for back scatter. In the momentum equations, a homogeneously constant value <C>xyz (varying in time) is used, which is computed by requiring that, when integrating over the whole computational domain, <C>xyz should give the same production as the local value C.
The model is applied to recirculating flow in an enclosure. The new model is shown to give better agreement with experimental data, to be considerably more stable numerically, and, as a consequence, to be computationally cheaper than the traditional, spanwise-averaging Germano model.
The idea is to include all local dynamic information through the source terms of the transport equation for ksgs. This is probably physically more sound since large local variations in C appear only in the source term, and the effect of the large fluctuations in the dynamic coefficients will be smoothed out in a natural way. In this way, it turns out that the need to restrict or limit the dynamic coefficient is eliminated altogether. The spatial variation of C is included via the production term in the modelled ksgs equation. In this way, back scatter is taken into account in an indirect way. Although it is not fed directly back to the resolved flow, it influences the resolved flow via the kinetic subgrid energy in two ways. First, a negative production reduces ksgs and thereby the subgrid viscosity. Second, a negative production also reduces <C>xyz.
An implicit, two-step time advancement method is used. When the filtered Navier-Stokes equation a velocity field is obtained which does not satisfy continuity. An intermediate velocity field is computed by subtracting the implicit part of the pressure gradient, and the resulting Poisson equation is solved employing an efficient multigrid method. Central differencing is used for the convective terms in all equations, including the ksgs equation. For more details, see [4,5].
A 64-processor Origin 2000 Silicon Graphics machine was used. The code has been parallelized by Zacharov [6]. For a backward-facing step (maximum CFL approximately 2), the achieved speed-up on 4 (8) processors is 3.5 (6.3) on a 1.3 million node mesh Each time step requires 28 seconds of CPU time on eight processors.

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  1. L. Davidson, Large Eddy Simulations: A Note on Derivation of the Equations for the Subgrid Turbulent Kinetic Energies, Rept. 97/11, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg.
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  2. L. Davidson, LES of Recirculating Flow Without Any Homogeneous Direction: A Dynamic One-Equation Subgrid Model, "2nd Int. Symp. on Turbulence Heat and Mass Transfer" pp. 481--490, Delft University Press, Delft, 1997.
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  3. L. Davidson, Large Eddy Simulation: A Dynamic One-Equation Subgrid Model for Three-Dimensional Recirculating Flow, "11th Int. Symp. on Turbulent Shear Flow, Grenoble" Vol. 3, pp. 26.1--26.6, Grenoble, 1997.
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  4. P. Emvin and L. Davidson, Development and Implementation of a Fast Large Eddy Simulations Method, Rept., Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, 1997.
  5. P. Emvin, The Full Multigrid Method Applied to Turbulent Flow in Ventilated Enclosures Using Structured and Unstructured Grids, Ph.D. thesis, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, 1997.
  6. I. Zacharov, private communication, European Supercomputer Team, Silicon Graphics Inc., Switzerland, 1997.
  7. L. Davidson and P. Nielsen
    "Study of Low-Reynolds Number Effects in Backward-Facing Step Flow Using Large Eddy Simulations", 6th Int. Conf. on Air Distributions in Rooms, ROOMVENT'98, Eds: E. Mundt & T.G. Malmström Vol. 1, pp. 125-132, Stockholm, Sweden, July 1998.
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  8. A. Sohankar, L. Davidson and C. Norberg
    "A Dynamic One-Equation Model for Simulation of Flow Around a Square Cylinder", Engineering Turbulence Modelling and Experiments -- 4, pp. 227--236} W. Rodi and D. Laurence (Editors), 1999.
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  9. S. Krajnovic, D. Müller and L. Davidson
    "Comparison of Two One-Equation Subgrid Models in Recirculating Flows", Direct and Large-Eddy Simulation III, pp. 63-74, Eds: P.V. Voke, N.D. Sandham & L. Kleiser
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  10. S. Krajnovic. and Davidson
    Large-Eddy Simulation of the Flow Around a Surface-Mounted Cube Using a Dynamic One-Equation Subgrid Model (to be presented)", The First International Symp. on Turbulence and Shear Flow Phenomena, pp. 741-746, Eds: S. Banerjee & J.K. Eaton, begell house, inc., New York, Wallingford U.K., 1999.
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  11. A. Sohankar, L. Davidson and C. Norberg.
    "Large Eddy Simulation of Flow Past a Square Cylinder: Comparison of Different Subgrid Scale Models", ASME J. Fluids Engng., Vol. 122, No. 1, pp. 39-47, 2000. (see also Erratum, ASME J. Fluids Engng., Vol. 122, No. 3, p. 643, 2000)


Inga-Lena Ljungström