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Solution time for p equation vs. U equations

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Old   July 15, 2020, 11:09
Default Solution time for p equation vs. U equations
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Hi All,

I have a general question about the typical time required to solve the U equations vs. the p equations in a CFD solution. I know from experience and reading some literature that it is typical for a CFD solver to spend most of the time (~80%) solving for pressure, but I am curious as to why this is the case.

If more specifics are required, I am considering the segregated solvers typically implemented in OpenFOAM, e.g. SIMPLE. PIMPLE, etc. which utilize the pressure-correction methodology (where the pressure correction is obtained from the Poisson equation of the divergence of the velocity)

Is this a result of the general nature (numerical properties) of elliptic PDEs (such as the Poisson equation), or is more specific to the algorithm (e.g. SIMPLE)?

Can anyone point to some good references on this topic?
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Old   July 19, 2020, 05:41
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You need to consider 3 apsects:

1) The two set of equations are solved multiple times, once per outer iteration, each one being around a linearization at the previous iteration. So, in general, it isn't really that useful to solve them very tightly because that problem you are solving is not the final one, but only an intermediate step.

2) The pressure equation is special in segregated solvers, because the pressure gradient is needed to satisfy the continuity equation. That is, in a way or another, the pressure gradient enters the mass fluxes used to transport all other variables.

3) Now, as conservation is one of the great advantages of FV, it turns out you don't want to throw it away during iterations. That is, even if you are solving the momentum equations only approximately, you want to do that with a mass preserving mass flux. In order to do that you need the accurate resolution of the pressure equation
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pde type, simple algorithm, solve pressure

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