TY - JOUR
T1 - Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes
AU - Kong , Wang
AU - Hong , Zhenying
AU - Yuan , Guangwei
AU - Sheng , Zhiqiang
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 402
EP - 427
PY - 2022
DA - 2022/12
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0280
UR - https://global-sci.org/intro/article_detail/aamm/21274.html
KW - Extremum-preserving correction, diffusion equation, distorted mesh, nine-point scheme.
AB - <p style="text-align: justify;">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.</p>