期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 37, 期 1, 页码 A420-A438出版社
SIAM PUBLICATIONS
DOI: 10.1137/140972470
关键词
diffusion equation; positivity-preserving property; linearity-preserving criterion
资金
- National Natural Science Foundation of China [11271053, 91330205, 11471047, 91130107]
- Foundation of President of China Academy of Engineering Physics [2014-1-042]
We propose a new positivity-preserving finite volume scheme for the anisotropic diffusion problems on general polygonal meshes based on a new nonlinear two-point flux approximation. The scheme uses both cell-centered and cell-vertex unknowns. The cell-vertex unknowns are treated as auxiliary ones and are computed by two second-order interpolation algorithms. Due to the new nonlinear two-point flux formulation, it is not required to replace the interpolation algorithm with positivity-preserving but usually low-order accurate ones whenever negative interpolation weights occur and it is also unnecessary to require the decomposition of the conormal vector to be a convex one. Moreover, the new nonlinear two-point flux approximation has a fixed stencil. These features make our scheme more flexible, easy for implementation, and different from other existing nonlinear schemes based on Le Potier's two-point flux approximation. The positivity-preserving property of our scheme is proved theoretically and numerical results demonstrate that the scheme has nearly the same convergence rates as compared with other second-order accurate linear schemes, especially on severely distorted meshes.
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