Further reading
L. Davidson, "Derivations
of some Stability Conditions Using von Neumann Analysis"
In this short note Neumann stability analysis is used to show:
-
that a central differencing scheme is unstable;
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that both a second-order derivative and a fourth-order derivative are dissipative;
this is true for all the nth-order derivative, where
n
is even;
-
that the Crank-Nicolson scheme is stable.
In the final section, we also show that the Gauss-Seidel solver converges
if aP > sum( anb)
J. Larsson, "A
Note on Numerical Errors"
This note talks about:
-
basic explanation of the effects different spatial derivatives have on
a solution
-
how numerical schemes are designed to a certain order
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why the discretisation of the viscous term is rarely discussed in the literature
-
why the discretisation of the convective term has a strong effects on the solution
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that upwinding and explicit addition of an even derivative are equivalent
-
Fourier analysis of the discretisation errors
-
how finite difference schemes can be transfered to finite volume schemes
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