2nd derivative on nonorthogonal FV-mesh
Hi, I'm trying to implement an nonlinear boussinesq model to a FV-code. The nonlinear model is from Speziale (see "On nonlinear models of turbulence", Journ. Fl. Mech, 1986 I think) and contains terms with second derivatives of the velocity. How is it possible to calculate the second derivative in 2D on a nonorthogonal FV-mesh, especially at the boundaries, and how to avoid oscillatory solutions ?
Re: 2nd derivative on nonorthogonal FV-mesh
Sorry for the late reply. When you use the FV approach, you should integrate your equations in the first step. The integrals over volume should be converted to the integrals over surfaces which normally leads to decreasing the orded of the integrand by one. Then your problem will be only to supply the approximation for the first derivative, which should not be a problem. To calculate the derivative on the boundary, I would calculate it either from the appropriate boundary conditions. If you're talking about the surface of the inner element, then you can calculate the cell-centered derivative, and then move it to the cell face either by interpolation or by the expansion in Taylor series from the cell center.
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