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?

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

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 ...

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

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

http://link.springer.com/article/10....0009-0?LI=true

A different approach is advocated in this paper

http://www.sciencedirect.com/science...21999108000429

where the reconstruction process is modified to get well behaved schemes in low mach limit. A similar approach is given here

http://elib.dlr.de/76675/1/ICCFD7-2204_paper.pdf