


Paper's Title:
Finite Volume Approximation of a Class of 2D Elliptic Equations with Discontinuous and Highly Oscillating Coefficients
Author(s):
J. D. Bambi Pemba and B. Ondami
Université Marien Ngouabi
Factuté des Sciences et Techniques
BP 69 Brazzaville,
Congo.
Email: bondami@gmail.com
URL:
https://www.researchgate.net/profile/BienvenuOndami
https://www.linkedin.com/in/bienvenuondami
Abstract:
In this paper, we are interested in the Finite Volume approximation of a secondorder twodimensional elliptic equation in heterogeneous porous medium with a periodic structure. The equation's coefficients are therefore discontinuous and highly oscillating. This class of problems has been extensively studied in the literature, where various methods proposed for determining the socalled homogenized problem. What we are particularly interested in is the direct numerical approximation of the problem, which has received little attention in the literature. We use the cellcentered finite volume approach for this purpose. Error estimates are established, and numerical simulations are conducted for both the isotropic and anisotropic media cases. The obtained solution is compared to the homogenized solution, and the results show that this approach provides an adequate approximation of the exact solution.
Paper's Title:
Numerical Approximation by the Method of Lines with Finitevolume Approach of a Solute Transport Equation in Periodic Heterogeneous Porous Medium
Author(s):
D. J. Bambi Pemba and B. Ondami
Université Marien Ngouabi,
Factuté des Sciences et Techniques,
BP 69, Brazzaville,
Congo.
Email: bondami@gmail.com
Abstract:
In this paper we are interested in the numerical approximation of a twodimensional 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 socalled 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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