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Center for Nonlinear Studies |
We consider the cell-centered finite volume discretization of the steady diffusion and convection-diffusion equations [1,2]. The diffusion tensor may be heterogeneous, full and essentially anisotropic. The convection-diffusion operator may have the dominated convection part. The conformal computational mesh is assumed to consist of convex polyhedral cells. The cornerstone of the method is the nonlinear two-point discretization of diffusion and advection fluxes derived on faces of mesh cells. The proposed finite volume method is monotone, i.e. it preserves non-negativity of the differential solution. The method is the 3D extension of the 2D finite volume discretizations
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