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I have been investigating smoothed-particle hydrodynamics (SPH) method. I read about two approach in this method: Weakly Compressible SPH (WCSPH) and Fully Incompressible SPH method. In WCSPH method density variations are less than 1%. Is it possible to simulate compressible flows using SPH with larger density variations, or where Mach number is grater than 0.3?

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  • $\begingroup$ I know some astrophysical SPH codes that handle large Mach number flows, but I don't know which of those two methods you mention these are $\endgroup$ – Kyle Kanos Dec 4 '16 at 23:14
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It is possible to simulate larger density variations. However, in case of too much compressibility, the so-called particle clustering will occur with kernels of higher than second order. Furthermore, the number of neighbours may become too much, resulting in "over-smoothing". Both of these problems could be solved by adaptively varying influence radii.

SPH is not so efficient in case of flows with large Re. On the one hand, it will require small time step to avoid the particles to advance to much between two steps, while on the other hand, non-physical void areas can be easily developed at low-pressure areas like inside the separation bubbles. A possible solution to circumvent this problem is the application of a background pressure, which unfortunately further reduces the required time step.

A short note:

SPH and for example FVM (finite volume method) are not competing numerical methods. They are both strong in cases where the other is weak. Highly compressible and large Reynolds number flows are typically not in the line of SPH.

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