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Separating velocity gradient terms as "grad(U)" and "gradUConv" in fvSchemes

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Old   December 15, 2023, 13:28
Exclamation Separating velocity gradient terms as "grad(U)" and "gradUConv" in fvSchemes
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atakan
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Hello everyone,

Regarding fvSchemes and especially the linearUpwind schemes, do you think separating the velocity gradient where one of them being used in linearUpwind interpolation (for convection terms) and the other one being used in actual physical gradient calculation at faces (such as velocity gradients in viscous stresses/diffusive fluxes) makes sense? I am interested in trying this out since the articles below state that leastSquares can get inaccurate for highly-stretched viscous meshes especially for curved surfaces and it is better to use it just in the interpolation of convective fluxes and let the viscous fluxes gradient be calculated with Green-Gauss theorem.

Reference articles:
1. https://arc.aiaa.org/doi/10.2514/6.2003-3986
2. https://ntrs.nasa.gov/citations/20090007493

What I mean is this:

gradSchemes
{
...
grad(U) cellLimited Gauss linear 1.0;
gradUConv cellLimited leastSquares 1.0;
...
}

divSchemes
{
...
div(phi,U) bounded Gauss linearUpwind gradUConv;
...
}

Many thanks and best regards,
Atakan
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finite volume method, fvschemes, grad u, gradient accuracy, gradient scheme

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