Can anyone advice me on the speed of sound? I am solving compressible flows. In doing, I have some troubles when the computation goes long. At that time, the fluid flow looks like incompressible state(i.e, density variation in space is negligible). I guess that the stability problem is related to the phase chage from compressible to incompressible. CFD people said that in incompressible state, the speed of sound becomes larger so that the CFL number needs a smaller time step size.

In this statement, I wonder followings

1. sound speed is variable or fixed. In acoustics, it is fixed at fixed temper... e.g., water is about 1500m/s

2. why compressible solver suffers from stability problems

3. Can incompressible sovler solve compressible problems?

If yes, why people has used compressible solver instead of incompressible solver which has wider application.

Thanks in advance. Before my final defense, I would like to clear this issue.

1. The speed of sound becomes infinite in the incompressible limit.

2. Infinite speed of sound is likely the source of your instability and the reason compressible solvers are very inefficient for approximating incompressible flow.

3. no

Jed

usually, if the Mach no. is in low subsonic (0<M<0.3) range, Using Incompressible codes with the assumption of incompressible fluid is preffered. the problem of low mach numbers in compressible codes is well known. generally, the compressible flow is considered as that having M>0.3 in engineering cases. so the codes are developed for this range appropriately!

1. Sound speed is sqrt(dP/dRho) at constant entropy. It varies with material and temperature. However, in case of the constant density assumption, the above relationship is infinite.

2. Compressible solver solves for density as one of the variables. Quite naturally, when the density variations with pressure are very small it encounters problems.

3. Yes, incompressible (SIMPLE family based) solver can solve compressible problem. However, its application is limited to relatively modest Mach numbers (less than 3-4) and the shock resolution may not be as good. I guess, this explains why people use compressible solver for high Mach number flows. At the same time, if flow is transsonic and/or areas with slow velocity are encountered in the doman the incompressible solver with some corrections is adviseable.