Splitting Methods For Solving Multi-Component Transport Model: A Multicomponent Mixture for Hydrogen Plasma

TL;DR

This paper introduces splitting algorithms for efficiently solving complex multicomponent transport models in plasma simulations, particularly for hydrogen plasma, improving numerical stability and computational efficiency.

Contribution

The paper presents novel noniterative and iterative splitting methods tailored for solving the nonlinear Stefan-Maxwell equations in multicomponent plasma transport models.

Findings

Iterative splitting methods improve solution accuracy.

Splitting methods relax nonlinear term complexities.

Numerical experiments demonstrate method benefits.

Abstract

In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that are used for medical and technical applications in etching processes. These multi-component transport-mixture models can be derived by approximately solving a linearised multi-component Boltzmann equation with an approximation of the collision terms in the mass, momentum and energy equations. The model-equations are nonlinear partial differential equations and they are known as Stefan-Maxwell equations. However, these partial differential equations are delicate to solve and we propose to use noniterative and iterative splitting methods. In the numerical experiments, we see the benefit of the iterative splitting methods, while these methods can relax the nonlinear terms.