Computation of effective transport coefficients of a microscale gas flow
by Pierre Charrier   Bruno Dubroca   Christophe Preux  

Vol. 2 No. 2 (2007) P.297~P.328

ABSTRACT

The aim of the present paper is to propose efficient numerical methods for solving linear kinetic problems arising in the modeling of heat and mass transport in porous media. We propose a Galerkin approximation for the velocity variables (which can be also interpreted as a moment method in some cases), and a classical finite-volume approximation for the space variables. The Galerkin approximation for the velocity variables reduces the linear kinetic equation to a linear hyberbolic system of dimension $N$, where $N$ is the number of basis functions used in the Galerkin method. To be ecient the approach must give correct prediction with small $N$. This can be obtained by a convenient choice of the basis functions which is governed by a mathematical analysis taking into account the physical regime. A modification of the space approximation is proposed to enforce the correct behavior in the fluid limit. Comparison of numerical results obtained by our method and direct solution of kinetic systems or experimental data are provided.

KEYWORDS
Porous media, microdevices, homogeneization, asymptotic preserving scheme, kinetic theory, eective transport coecients

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 76M45, 76M50, 76P05, 76R05, 76S05, 82C40, 82C70

MILESTONES

Received: 2004-11-29
Revised : 2005-06-03
Accepted:

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