Numerical Methods of the Maxwell-Stefan Diffusion Equations and Applications in Plasma and Particle Transport

Abstract

In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan model, which describe multicomponent diffusive fluxes in the gas mixture. Based on additional conditions to the fluxes, we obtain an irreducible and quasi-positive diffusion matrix. Such problems results into nonlinear diffusion equations, which are more delicate to solve as standard diffusion equations with Fickian's approach. We propose explicit time-discretisation methods embedded to iterative solvers for the nonlinearities. Such a combination allows to solve the delicate nonlinear differential equations more effective. We present some first ternary component gaseous mixtures and discuss the numerical methods.