Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes

被引：144

作者：

Le Potier, C ^{[1
]}

机构：

[1] Commissariat Energie Atom, DEN, DM2S, SFME,MTMS, F-91191 Gif Sur Yvette, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2005年 / 341卷 / 12期

关键词：

D O I：

10.1016/j.crma.2005.10.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new finite volume method for highly anisotropic diffusion operators on unstructured meshes. The main idea is to calculate the gradient using a nonlinear scheme. For parabolic problems, if the time step is small enough. the resulting global matrix is monotone without geometrical constraints on the mesh and restrictive conditions on the anisotropy ratio. We check the precision of the method in comparison with analytical Solutions. The efficiency of the algorithm is demonstrated by comparing it with numerical schemes which do not satisfy a discrete maximum principle on the studied case.

引用

页码：787 / 792

页数：6

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