[paulzhang]

Hello,

This is Paul Zhang again. I was a centroid-centerd FVM guy and I am now being updated to vertex-centered median-dual scheme.

My question comes from the computation of viscous fluxes normal to the face. Say, we have node i and j, which are two nodes, and we want to find the viscous fluxes across the face which is formed by two cell centroids on both sides of line i-j and the mid-point of line i-j. So there should be two sub-faces with two face normals and face areas.

Eqn 35, page 21 of paper "Stanford University Unstructured (SU2): An open-source integrated computational environment for multi-physics simulation and design.", however, only has one face normal used. Is this just an approximation? What is the justification for that?

Thanks,
Paul

[fpalacios]

Dear Paul,

Thanks for using SU2. This is a good question... and you are correct, it is not clear in the article.
(35) is the method that SU2 uses to compute the normal component, the tangent component is computed by subtracting the normal component to the gradient computed using Green-Gauss or LS.

You can find the implementation in
void CAvgGradCorrected_Flow::ComputeResidual(su2double *val_residual, su2double **val_Jacobian_i, su2double **val_Jacobian_j, CConfig *config) { }
inside numerics_direct_mean.cpp

Once you have the gradient you will suit to evaluate F_V (Eq. 2) and then you project that into the normal vector to evaluate the volumen integration (weak formulation) via the Gauss Theorem (surface integral).

And yes, in a median dual scheme there are two normals (2D) that we add together to only a normal to each edge.

Best,
Francisco