Viscous term expansion
Hi all, I'm studying the implementation of the viscous term in NS equations in the general framework used for example in pisoFoam, nevertheless I can't understand some of the things that are done. Viscous term is:
due incompressibility and applying div to the product, it becomes
laplacian(nuEff, U)+ grad(nuEff)*[(grad(U)+grad(U)^T)] (1)
in laminar regime nuEff=nu and in turbulent regime nuEff=nu+nut. Reading the code we have from pisoFoam.C:
All ideas are welcome.
Perhaps you have it already solved, but here goes my try:
The laminar part of viscous stress tensor is:
The turbulent part of viscous stress tensor is
Now, summing both contributions:
The last term in OpenFOAM code is not the same, though:
- it is computed the deviatoric of and not the gradient itself. This is discussed in another topic: http://www.cfd-online.com/Forums/ope...ivdevreff.html
The trace of last term is zero because of the explicit formulation using the velocity field from previous time step, that should be divergence free.
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