Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, we construct a new cell-centered nonlinear finite volumescheme that preserves the extremum principle for heterogeneous anisotropic diffusionequation on distorted meshes. We introduce a new nonlinear approach to constructthe conservative flux, that is, a linear second order flux is firstly given and a nonlinearconservative flux is then constructed by using an adaptive method and a nonlinearweighted method. Our new scheme does not need to use the convex combination ofthe cell-center unknowns to approximate the auxiliary unknowns, so it can deal withthe problem with general discontinuous coefficients. Numerical results show that ournew scheme performs more robust than some existing schemes on highly distortedmeshes.