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Solver-guidance: Dilatable or fully compressible?

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Old   September 21, 2012, 04:46
Default Solver-guidance: Dilatable or fully compressible?
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Bernhard Linseisen
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Dear all,

at the moment I am starting some simulations which certainly will become compressible at some point (Ma >> 0.3).

If I am informed correctly, there are two ways density can be influenced, either via the ideal gas law or via velocity in addition. The first case would be called dilatable, the second one fully compressible.

Unfortunately also the existing documentation does not tell which solvers are working dilatable and which one work fully compressible. Thus at least here I would like to establish a small list which solvers fulfill which criteria. Please help out as well, if possible!
I will update the list with information in this first post.

The list of socalled compressible solvers I put below is compiled from both versions of OpenFoam, the 1.6-ext and the 2.0.x releases...

Solvers are:


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Old   September 21, 2012, 05:00
Default How to know?
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Bernhard Linseisen
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As I certainly do want to contribute as well: Can someone tell me definite criteria for the solver to be dilatable or fully compressible?

Of course the best would be to get a short description why a specific solver should be regarded fully compressible or dilatable only.
For me the default assumption would be that any solver not proven fully compressible is dilatable...
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Old   September 24, 2012, 06:02
Franco Marra
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Dear all,

I too do not have the answer, but maybe I can try to provide some indications.

Probably it is necessary to check how the different solvers treat the propagation of sound waves. Strictly speacking, fully compressible solvers should be able to fully resolve sound waves. This is usually the case for so called density based solvers (rhoSonicFoam ?) that explicity integrate in time the density equation, recovering the pressure from the equation of state.

This approach, very commonly adopted for supersonic flow, is not suitable when dealing with many cases of weackly (Mach < 1) compressible flows, as it would require too small time steps with respect to the time scale of the phenomena and because of numerical issues arising from the disparity of flow velocity with respect to sound speed.

Now, several approach exists to deal with this type of problems. If the Mach number is very low (Mach << 0.3) but large density gradients occurs because of the presence of strong heat addition (like in many combustion systems) compressibility effects (from pressure waves) are negligible with respect to thermal expansion, in the sense that compressibilty equilibrates much faster than thermal expansion.
Some solvers use this property to solve a different set of equations based on asimptotic expansion with respect to the Mach number. They are therefore unable to include real compressibility, but they solve the thermal expansion with a great gain in computational demand and stability. I think that fireFoam is probably based on these assumptions.

Otherwise, in the case that both effects are present (thermal expansion and sound wave compressibility, Mach <1), there are solvers that, without modifying the original formulation, use an iterative procedue that solve the numerical issues arising from the disparity of scales. I am not really sure, but I understood that, by deriving an elliptic equation for the pressure, you are able to find a pressure field that equilibrate the flow at a time step longer than that required to fully resolve the sound wave propagation. This probably means that this class of solvers, if used with small enough time steps, should be able to recover a fully compressible solution, while, if adopted with larger time steps, allow for an efficient computation of weakly compressible flows. If my ideas are correct (plese help me to check this issue) many of the solvers based on the solution of an elliptic pressure equation like rhoSimpleFoam and rhoPimpleFoam, should fall in this class.

I am sorry I do not have a definitive answer, but I hope the this can contribute to form a scheme for the classification of the solvers.

My best regards to all,

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