Splitting Approach for Solving Multi-Component Transport Models with Maxwell-Stefan-Diffusion

TL;DR

This paper introduces splitting algorithms for efficiently solving multicomponent transport models with Maxwell-Stefan diffusion, particularly in plasma processes, by decomposing complex equations into manageable parts and employing iterative methods.

Contribution

The paper presents novel splitting algorithms tailored for multicomponent Maxwell-Stefan diffusion models, enhancing numerical efficiency in plasma transport simulations.

Findings

Splitting methods improve convergence in nonlinear multicomponent diffusion problems.

Combining iterative splitting with nonlinear solvers relaxes nonlinear term constraints.

Numerical experiments demonstrate the effectiveness of the proposed approach.

Abstract

In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the local thermodynamic equilibrium and weakly ionized plasma-mixture models are given. Such processes are used for medical and technical applications. These multi-component transport modelling equations are related to convection-diffusion-reactions equations, which are wel-known in transport processes. The multicomponent transport models can be derived from the microscopic multi-component Boltzmann equations with averaging quantities and leads into the macroscopic mass, momentum and energy equations, which are nearly Navier-Stokes-like equations. We discuss the benefits of the decomposition into the convection, diffusion and reaction parts, which allows to use fast numerical solvers for each part. Additional, we concentrate on the nonlinear parts of the multicomponent diffusion, which can be effectively solved with iterative splitting approaches In the numerical experiments, we see the benefit of combining iterative splitting methods with nonlinear solver methods, while these methods can relax the nonlinear terms. In the outview, we discuss the future investigation of the next steps in our multicomponent diffusion approaches.