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A positivity-preserving finite volume scheme for diffusion equations on polyhedral meshes. (Chinese. English summary) Zbl 1340.76055

Summary: We construct a nonlinear cell-centered finite volume scheme for diffusion equations on star-shaped polyhedral meshes and prove that it is positivity-preserving. Based on harmonic average point, we design a new locally explicit weighted method to calculate intermediate unknowns, including the vertex and face unknowns. Our scheme is applicable for distorted meshes with cell-faces being non-plane, and suitable for diffusion problems with discontinuous coefficient. Numerical examples verify the convergence and positivity of numerical solution of our scheme.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
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