The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Numerical Approximation by the Method of Lines with Finite-volume Approach of a Solute Transport Equation in Periodic Heterogeneous Porous Medium


D. J. Bambi Pemba and B. Ondami

Université Marien Ngouabi,
Factuté des Sciences et Techniques,
BP 69, Brazzaville,


In this paper we are interested in the numerical approximation of a two-dimensional solute transport equation in heterogeneous porous media having periodic structures. It is a class of problems which has been the subject of various works in the literature, where different methods are proposed for the determination of the so-called homogenized problem. We are interested in this paper, in the direct resolution of the problem, and we use the method of lines with a finite volume approach to discretize this equation. This discretization leads to an ordinary differential equation (ODE) that we discretize by the Euler implicit scheme. Numerical experiments comparing the obtained solution and the homogenized problem solution are presented. They show that the precision and robustness of this method depend on the ratio between, the mesh size and the parameter involved in the periodic homogenization.

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