# Compressible Navier--Stokes for incompressible cases

**URL:** <https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600>\
**Category:** General\
**Created:** [8 May 2022 02:49 UTC](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600 "2022-05-08T02:49:40Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![randommc](https://avatars.discourse-cdn.com/v4/letter/r/e56c9b/32.png) [@randommc](https://pyfr.discourse.group/u/randommc)\
**Post date:** [8 May 2022 02:49 UTC](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600/1 "2022-05-08T02:49:40Z")

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Thank you very much. I have another question. I want to simulate TGV at Re=1600, Ma=0.08. Can compressible N-S solver be used to simulate incompressible problems directly without ACM?

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**Author:** ![WillT](https://avatars.discourse-cdn.com/v4/letter/w/bc79bd/32.png) [@WillT](https://pyfr.discourse.group/u/WillT)\
**Post date:** [9 May 2022 07:47 UTC](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600/2 "2022-05-09T07:47:46Z")

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I moved this post here as it was a bit off topic.

You can, although as you approach the incompressible limit the simulation will become increasingly stiff. For the TGV, M=0.08 is standard and will work fine with compressible Navier–Stokes. However, using compressible for incompressible cases in general — like most things in CFD — is case dependent and dependent on what you are trying to investigate.

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**Author:** ![randommc](https://avatars.discourse-cdn.com/v4/letter/r/e56c9b/32.png) [@randommc](https://pyfr.discourse.group/u/randommc)\
**Post date:** [9 May 2022 08:08 UTC](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600/3 "2022-05-09T08:08:04Z")

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Thank you for your reply. I also see the Ma is set to be 0.1 in many articles, could I compare the results of Ma=0.08 with Ma=0.1?

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**Author:** ![WillT](https://avatars.discourse-cdn.com/v4/letter/w/bc79bd/32.png) [@WillT](https://pyfr.discourse.group/u/WillT)\
**Post date:** [9 May 2022 08:15 UTC](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600/4 "2022-05-09T08:15:26Z")

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I don’t know this for sure, but often when people state the Mach number for the TGV as 0.1, it’s actually ~0.081. But even if it where 0.1, the difference I think would be negligible. I actually looked at the effect of compressibility a little bit for the TGV in this paper: [Effect of Flux Function Order and Working Precision in Spectral Element Methods | AIAA SciTech Forum](https://doi.org/10.2514/6.2020-0566)

This wasn’t the main point of the paper, but I compare M=0.081 to M=0.3. The difference isn’t huge, and actually other things effect the result more that compressibility.