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

TL;DR

This paper develops and tests numerical methods for solving nonlinear Maxwell-Stefan diffusion equations in plasma and particle transport, with applications in etching processes, emphasizing effective explicit time discretization and iterative solvers.

Contribution

It introduces explicit time-discretization methods combined with iterative solvers for nonlinear Maxwell-Stefan equations in plasma modeling, improving computational efficiency.

Findings

Successfully applied methods to ternary gaseous mixtures.

Demonstrated effectiveness of explicit discretization in nonlinear problems.

Discussed numerical stability and convergence of the proposed algorithms.

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.