Positivity of Discrete Laplacian on Triangular Grids with Arbitrary Angles

Finite volume approximation to Laplace equation on unstructured grids with general geometry of cells is considered. Given order of reconstruction, the reasons of appearing negative coefficients in the scheme are investigated. The procedure of stencils correction for getting a positive scheme with linear reconstruction on arbitrary triangulation is developed. Numerical experiments on a model mesh show that the corrected scheme is positive for any value of the mesh maximum angle, unlike the standard finite volume discretization used before. A hypothesis about generalization of a Delaunay criterion in the case of higher order reconstruction is formulated.