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HR Scheme inplementation in OpenFOAM

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Old   June 22, 2017, 06:30
Default HR Scheme inplementation in OpenFOAM
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Nuno Enes
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Hi everyone,

For a while now I have been interested to understand how the QUICK scheme is implemented in OpenFOAM. I gathered so far (please correct me if I am wrong) that it is formulated as a TVD scheme such that the flux at face phi_f is,

phi_f = phi_C + 0.5*psi(r)*(phi_D - phi_C)

where the subscripts f,C and D correspond to the values at the face, the upwind node (relative to the face) and the downwind node respectively.

However when I read the code in "QUICK.H" where the limiter is defined i find,

phiCD = cdWeight*phiP + (1 - cdWeight)*phiN;

phif = 0.5*(phiCD + phiP + (1 - cdWeight)*(d & gradcP));

and the limiter which I assume is given by QLimiter

psi(r)=QLimiter = (phif - phiU)/stabilise(phiCD - phiU, SMALL);

In OpenFOAM notation I think node C = P and D = N (for the case of east-bound flow)

I am puzzled by this. I suspect phi_f is being calculated via QUICK scheme's gradient form,

phi_f = phi_C + 0.5*(nabla(phi_C) + nabla(phi_f)).d_Cf

But that is where I am at.

Could somebody enlighten me?

Thank you!
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interpolation, quick, scheme

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