Extremum-preserving correction of the nine-point scheme for diffusion equation on distorted meshes
- DOI number:10.4208/aamm.OA-2021-0280
- Journal:Advances in Applied Mathematics and Mechanics
- Key Words:Extremum-preserving correction, diffusion equation, distorted mesh, nine-point scheme
- Abstract:In this paper, we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes. We introduce a new nonlinear approach to construct the conservative flux, that is, a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method. Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns, so it can deal with the problem with general discontinuous coefficients. Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.
- Indexed by:Unit Twenty Basic Research
- Discipline:Natural Science
- First-Level Discipline:Mathematics
- Document Type:J
- Volume:15
- Issue:2
- Page Number:402-427
- Translation or Not:no
- Included Journals:SCI
- Date of Publication:2023-01-04
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