Iterative solvers for the Maxwell-Stefan diffusion equations: Methods and applications in plasma and particle transport

In this paper, we are motivated to discuss a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. For studying the model, we consider a simplified model based on the Maxwell-Stefan model, which describes multicomponent diffusive fluxes in the gas mixture. The MS model is more adequate to describe complex mixtures without dominating background species. Based on additional conditions to the fluxes, we obtain an irreducible and quasi-positive diffusion matrix. Such problems result in nonlinear diffusion equations, which are more delicate to solve as simpler standard diffusion equations with Fickian's approach. Here, we propose an efficient explicit time-discretization method, which is embedded to a fast iterative solver for the nonlinearities. Such a combination of coupling discretization and solver methods allows to simulate the delicate nonlinear differential equations more effectively. We present the efficiency and accuracy of the iterative solvers for some first ternary component gaseous mixtures and discuss the details of the numerical methods.