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-   -   Compressible solver for low Mach (http://www.cfd-online.com/Forums/main/112331-compressible-solver-low-mach.html)

 nickna January 26, 2013 04:45

Compressible solver for low Mach

Dear all,
If anybody has the experience in using the compressible solver for very low Mach (thus almost incompressible) cases? Is it possible?
If yes, in principle the calculation can be much speeded up because we dont not need to solve the Poission eq for pressure.
If no, where is the main problem?

 FMDenaro January 26, 2013 06:32

Quote:
 Originally Posted by nickna (Post 404149) Dear all, If anybody has the experience in using the compressible solver for very low Mach (thus almost incompressible) cases? Is it possible? If yes, in principle the calculation can be much speeded up because we dont not need to solve the Poission eq for pressure. If no, where is the main problem? Many thanks for your suggestion!
Hi,
generally, the low-Mach solver is quite different from the standard compressible solver due to the stiff problem (high velocity magnitude of sound waves compared to convective waves).
The method to get a well-conditioned problem often introduces an expansion arounf the M=0 state and consequently an elliptic equation. You can see many textbook, e.g. http://books.google.it/books/about/C...4C&redir_esc=y

 cfdnewbie January 26, 2013 07:16

But in general, yes, it is possible to use a compressible solver in a low Mach number setting, but the timestep will become very small (or the accuracy very low)...

 FMDenaro January 26, 2013 07:37

Quote:
 Originally Posted by cfdnewbie (Post 404161) But in general, yes, it is possible to use a compressible solver in a low Mach number setting, but the timestep will become very small (or the accuracy very low)...
I agree, even small perturbations in the numerical solution of the density equation will be amplified in the pressure ... I had experience that the Mach number to work on should be not lesser than 0.1 - 0.05 ...

 Martin Hegedus January 26, 2013 22:40

Yes, it is possible with Mach number preconditioning. But, you lose time accuracy.

 praveen January 27, 2013 05:23

There is a preconditioned Roe scheme in which the dissipation is modified to yield correct scheme in the low mach limit. There is also an AUSM version which performs well in low mach limit but I dont recall its precise name now. These are all consistent flux functions which lead to time accurate schemes. However they require very small time step for stability and implicit schemes are necessary. E.g., SU2 code has a preconditioned Roe scheme.

See for example

http://www.sciencedirect.com/science...45793003000781

which has a very nice asymptotic analysis of upwind schemes in low mach limit.

In the following paper, they show that above preconditioned scheme if used in explicit version requires time step of order mach^2 which is too restrictive and hence an implicit scheme is needed for efficiency