A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations

Laurent Boudin; Bérénice Grec; Francesco Salvarani

doi:10.3934/dcdsb.2012.17.1427

Article Contents

2012, Volume 17, Issue 5: 1427-1440. Doi: 10.3934/dcdsb.2012.17.1427

This issue Previous Article Time-averaging and permanence in nonautonomous competitive systems of PDEs via Vance-Coddington estimates Next Article Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions

A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations

1.
UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005
2.
INRIA Paris-Rocquencourt, REO Project team, BP 105, 78153 Le Chesnay

Received: May 31, 2010

Revised: May 31, 2011

Published: June 2012

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Abstract

We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. Mostly in the case of a tridiagonal diffusion matrix, we provide a qualitative and quantitative mathematical analysis of the model. We develop moreover a standard explicit numerical scheme and investigate its main properties. We eventually include some numerical simulations underlining the uphill diffusion phenomenon.

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Mathematics Subject Classification: Primary: 35Q35, 35B40; Secondary: 65M06.

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