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Peter May 7, 2003 15:52

Compressible code at low Mach numbers
Can a compressible code accurately predict the flowfield at low Mach numbers (below 0.25)?

Bob Roach May 8, 2003 05:21

Re: Compressible code at low Mach numbers
As opposed to what an incompressible flow code? It should be more accurate. For one, it does not make the incompressible assumption and hence takes into account the small but nonzero changes in density and temperature that exist in low speed flows.

BeachComber May 8, 2003 09:12

Re: Compressible code at low Mach numbers
As long as it has a good preconditioning method (to handle convergence), a compressible code can very well handle low speed flows to provide physical realistic and accurate results.

andy May 8, 2003 11:12

Re: Compressible code at low Mach numbers
It depends on the code. Some compressible codes tend towards the incompressible solution as the Mach number is reduced but some do not. If this was not a requirement when when your particular code was put together it would probably be safest to assume no. However, modifications to make the common compressible schemes behave correctly in the incompressible limit are usually available in the literature.

Mac May 10, 2003 00:56

Re: Compressible code at low Mach numbers
Of course whether this reduction to the incompressible limit is physical depends on the application. For example, in combustion the Mach number tends to be low (0.1 is typical of many applications), but the density can vary by a factor of around 5 due to various physical processes. Low Mach number is not always the same as incompressible.

Alexey May 15, 2003 05:26

Re: Compressible code at low Mach numbers
Yes of course. Correct compressible code must simulate low Mach flow correctly. Difficulty in this case is that the time step may be strongly limited due to stability condition for explicit scheme for very low Mach number (for example 0.01). But M=0.2 is good for explicit scheme. In general at low Mach number the flow does not depend on Mach number itself. Therefore flows with say M=0.1 and M=0.01 are the same in dimensionless form.

andy May 15, 2003 06:18

Re: Compressible code at low Mach numbers
I think "correct" may be a bit too strong for simulations in the real world and "appropriate" for given circumstances more reasonable.

One cannot sensibly run explicit compressible codes at low Mach numbers because the time step is limited by the sound speed as you point out (although for steady-state solutions one can reduce the sound speed to a degree). Generally, one needs to use implicit or semi-implicit schemes. The latter are fairly rare but are often targeted at low Mach number acoustic problems. The former are more common but are usually targeted at high Mach number flows. This is where practical problems arise because the pre-conditioning, dissipation, upwinding, etc... which needs to be introduced to create a robust scheme may be "tuned-up" for high Mach number flows. It is quite common for such "extra terms" to do the business at high Mach numbers but grow disproportionally at low Mach numbers and destroy the validity of the solution. I would suggest that such schemes are correct but are only applicable to high Mach number flows.

andy May 15, 2003 07:12

Re: Compressible code at low Mach numbers
I think it depends on what meaning one hangs on the label "incompressible". It is very common (should I go so far as to say usual?) to label codes as either "incompressible" or "compressible" depending on whether pressure gradients arise purely because of acceleration in the fluid ("incompressible" - no sound waves) or acceleration and compression ("compressible" - sound waves). This breaking of the link between pressure and compression being the assumption of incompressibility. Whether the density varies and the fluid dilatation is non-zero is not relevant to the assumption.

Now I admit it might be clearer to refer to "zero mach number" combustion codes rather than "incompressible" combustion codes and people do increasingly seem to be doing this. However, one does then end up with two different labels for the same assumption.

So is "low mach number" the same as "incompressible"?

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