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

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 investigateits main properties. We eventually include some numerical simulations underlining the uphill diffusion phenomenon.