A positive scheme for diffusion problems on deformed meshes

被引：43

作者：

Blanc, Xavier ^{[1
]}

Labourasse, Emmanuel ^{[2
]}

机构：

[1] Univ Paris Diderot, Lab Jacques Louis Lions, Batiment Sophie Germain,5 Rue Thomas Mann, F-75205 Paris 13, France

[2] CEA, DAM, DIF, F-91297 Arpajon, France

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2016年 / 96卷 / 06期

关键词：

Deformed mesh; finite volume; diffusion; maximum principle; numerical analysis; FINITE-VOLUME METHOD; TENSOR COEFFICIENTS; EQUATIONS; CONVERGENCE; OPERATORS; APPROXIMATION; DISCRETIZATION; RADIATION;

D O I：

10.1002/zamm.201400234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present in this article a positive finite volume method for diffusion equation on deformed meshes. This method is mainly inspired from [50, 52], and uses auxiliary unknowns at the nodes of the mesh. The flux is computed so as to be a two-point nonlinear flux, giving rise to a matrix which is the transpose of an M-matrix, which ensures that the scheme is positive. A particular attention is given to the computation of the auxiliary unknowns. We propose a new strategy, which aims at providing a scheme easy to implement in a parallel domain decomposition setting. An analysis of the scheme is provided: existence of a solution for the nonlinear system is proved, and the convergence of a fixed-point strategy is studied. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：660 / 680

页数：21

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