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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 187634, 23 pages
http://dx.doi.org/10.1155/2012/187634
Research Article

The Finite Volume Formulation for 2D Second-Order Elliptic Problems with Discontinuous Diffusion/Dispersion Coefficients

Dipartimento di Economia e Ingegneria Agraria, Forestale e Ambientale (DEIAFA) Sez. Idraulica, Via Leonardo da Vinci 44, 10095 Grugliasco, Italy

Received 18 July 2011; Revised 2 November 2011; Accepted 17 November 2011

Academic Editor: Moran Wang

Copyright © 2012 Stefano Ferraris et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a finite volume method for the numerical resolution of two-dimensional steady diffusion problems with possibly discontinuous coefficients on unstructured polygonal meshes. Our numerical method is cellcentered, secondorder accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.