Finite Volume Scheme Based on Cell-Vertex Reconstructions for Anisotropic Diffusion Problems with Discontinuous Coefficients

被引：0

作者：

Costa, Ricardo ^{[1
]}

Clain, Stephane ^{[1
]}

Machado, Gaspar Jose ^{[1
]}

机构：

[1] Univ Minho, Ctr Math, P-4800058 Guimaraes, Portugal

来源：

COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2014, PT 1 | 2014年 / 8579卷

关键词：

Finite volume; second-order; non-homogeneous and anisotropic diffusion; ADVECTION-DIFFUSION; APPROXIMATION;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We propose a new second-order finite volume scheme for non-homogeneous and anisotropic diffusion problems based on cell to vertex reconstructions involving minimization of functionals to provide the coefficients of the cell to vertex mapping. The method handles complex situations such as large preconditioning number diffusion matrices and very distorted meshes. Numerical examples are provided to show the effectiveness of the method.

引用

页码：87 / 102

页数：16

共 23 条

[1]

Berthon C., 2014, ESAIM MATH IN PRESS

[2] Least square-based finite volumes for solving the advection-diffusion of contaminants in porous media [J].

Bertolazzi, E ;

Manzini, G .

APPLIED NUMERICAL MATHEMATICS, 2004, 51 (04) :451-461

[3] On vertex reconstructions for cell-centered finite volume approximations of 2d anisotropic diffusion problems [J].

Bertolazzi, Enrico ;

Manzini, Gianmarco .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (01) :1-32

[4] Vertex-centroid finite volume scheme on tetrahedral grids for conservation laws [J].

Chandrashekar, Praveen ;

Garg, Ashish .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (01) :58-74

[5] A sixth-order finite volume method for multidomain convection-diffusion problem with discontinuous coefficients [J].

Clain, S. ;

Machado, G. J. ;

Nobrega, J. M. ;

Pereira, R. M. S. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2013, 267 :43-64

[6]

Costa R., NEW CELL VE IN PRESS

[7]

Coudière Y, 1999, RAIRO-MATH MODEL NUM, V33, P493

[8] A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids [J].

Domelevo, K ;

Omnes, P .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2005, 39 (06) :1203-1249

[9] Finite volume approximation of elliptic problems and convergence of an approximate gradient [J].

Eymard, R ;

Gallouët, T ;

Herbin, R .

APPLIED NUMERICAL MATHEMATICS, 2001, 37 (1-2) :31-53

[10] UPWIND SCHEME FOR SOLVING THE EULER EQUATIONS ON UNSTRUCTURED TETRAHEDRAL MESHES [J].

FRINK, NT .

AIAA JOURNAL, 1992, 30 (01) :70-77

← 1 2 3 →