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Conservative Flux in (in-)compressible PimpleFoam

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Old   March 30, 2022, 07:19
Question Conservative Flux in (in-)compressible PimpleFoam
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Adrian
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Hello Everyone,


i have recently gotten into CFD and i have been exploring the OpenFOAM source code a bit to better understand whats going on. Specifically, i have been looking into the incompressible/pimpleFoam and the compressible/rhoPimpleFoam solvers and i think by now i have a farely good grasp at what most of the code does. But there is one thing that strikes me as odd in the pressure equation sections of both solvers (pEqn.H):


After the pressure equation is solved, in the last non-orthogonal corrector loop the conservative flux
Code:
phi
is corrected. For the incompressible solver (pimpleFoam/pEqn.H) the corresponding code looks like this:


Code:
phi = phiHbyA - pEqn.flux();

which, from what i understand is equivalent to


\phi_f  = \boldsymbol S_f \cdot \left( \frac{H(\boldsymbol U)}{A_P} \right)_f -  \underbrace{\boldsymbol S_f \cdot \left( \frac{\boldsymbol \nabla  p}{A_P} \right)_f}_{\text{pEqn.flux}}


and becomes


\phi_f  = \boldsymbol S_f \cdot \left( \frac{H(\boldsymbol U)}{A_P} \right)_f -  \left( \bigl| \frac{\boldsymbol \Delta}{(A_p)_f} \bigr| \, \frac{p_N -  p_P}{d} + \frac{\boldsymbol k}{(A_p)_f} \cdot (\boldsymbol \nabla p)_f  \right)


where the surface element [math] S = \Delta + k [\math]. This is all good and i get where it is coming from. The problem lies in the comparison to the compressible solver (rhoPimpleFoam/pEqn.H):


Here, the correction to the conservative flux is written as


Code:
phi = phiHbyA + pEqn.flux();

so the sign of the
Code:
 pEqn.flux()
is flipped. As i understand it, the
Code:
.flux()
function should be functionally identical to the incompressible case, except that now the density \rho is a factor:


\phi_f =  \boldsymbol S_f \cdot \left( \rho \, \frac{H(\boldsymbol U)}{A_P}  \right)_f - \underbrace{\boldsymbol S_f \cdot \left( \rho \,  \frac{\boldsymbol \nabla p}{A_P} \right)_f}_{\text{pEqn.flux}}


\phi_f  = \rho_f \, \boldsymbol S_f \cdot \left( \frac{H(\boldsymbol U)}{A_P}  \right)_f - \left( \bigl| \left( \frac{\rho}{A_p} \right)_f \boldsymbol  \Delta \bigr| \, \frac{p_N - p_P}{d} + \left( \frac{\rho}{A_p} \right)_f  \boldsymbol k \cdot (\boldsymbol \nabla p)_f \right)


So if these equations are correct, then why is the sign for
Code:
pEqn.flux()
flipped in the compressible solver?




I hope this is the right forum for this question. Thx already in advance
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