Wang, Shuai; Hang, Xudeng; Yuan, Guangwei A positivity-preserving finite volume scheme for diffusion equations on polyhedral meshes. (Chinese. English summary) Zbl 1340.76055 Math. Numer. Sin. 37, No. 3, 247-263 (2015). 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. Cited in 2 ReviewsCited in 8 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics Keywords:polyhedral meshes; positivity-preserving scheme; harmonic average point; diffusion equations PDFBibTeX XMLCite \textit{S. Wang} et al., Math. Numer. Sin. 37, No. 3, 247--263 (2015; Zbl 1340.76055)