THE DISCRETE DUALITY FINITE VOLUME METHOD FOR CONVECTION-DIFFUSION PROBLEMS

被引：51

作者：

Coudiere, Yves ^{[1
]}

Manzini, Gianmarco ^{[2
]}

机构：

[1] Univ Nantes, CNRS, Lab Math Jean Leray, UMR 6629, F-44322 Nantes 3, France

[2] CNR, IMATI, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 47卷 / 06期

关键词：

convection-diffusion equation; discrete duality finite volume method; polynomial reconstruction; diamond scheme; unstructured meshes; polygonal meshes; CONVERGENCE ANALYSIS; UNSTRUCTURED MESHES; DIFFERENCE METHOD; SCHEME; OPERATORS; APPROXIMATION; EQUATIONS;

D O I：

10.1137/080731219

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we extend the discrete duality finite volume (DDFV) formulation to the steady convection-diffusion equation. The discrete gradients defined in DDFV are used to define a cell-based gradient for the control volumes of both the primal and dual meshes, in order to achieve a higher-order accurate numerical flux for the convection term. A priori analysis is carried out to show convergence of the approximation, and a global first-order convergence rate is derived. The theoretical results are confirmed by some numerical experiments.

引用

页码：4163 / 4192

页数：30

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