Spalart-Allmaras and "Non-Conservative Diffusion"
I'm an undergrad student and I'm implementing the S-A model for incompressible flow in a FV solver;
I have access to STAR-CCM+'s documentation and there I found an entry explaining that they did not discretize explicitly one of parcels of the diffusion term but that they combined it with the conservative diffusion one. I tried to get to the formula on my own using the identity:
And got a very similar result to STAR's:
Except that in the documentation it appears as a and the last term has, instead of the Laplacian, a which I assume is their mistake (is it?).
My questions are: a) is this common practice? and b) I'll treat the first term as a regular diffusion term with the diffusivity given by last iteration's , but how can I best discretize the last one? Explicitly calculate the laplacian on a cell by cell basis, multiply by and put the result in the right-hand side?
Any help apreciated.
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