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.

翻译：本文提出采用分裂算法求解基于Maxwell-Stefan扩散方法的多组分输运模型。该多组分模型涉及输运问题，重点考虑等离子体过程，其中包含局部热力学平衡与弱电离等离子体混合物模型。此类过程被应用于医疗及技术领域。这些多组分输运建模方程与对流-扩散-反应方程相关，后者在输运过程中广为人知。多组分输运模型可从微观多组分Boltzmann方程通过平均量推导得出，进而得到近乎Navier-Stokes形式的宏观质量、动量与能量方程。我们探讨了对流、扩散和反应部分分解的优势，该分解方式允许对每个部分使用快速数值求解器。此外，我们重点关注多组分扩散的非线性部分，这类问题可通过迭代分裂方法高效求解。数值实验表明，将迭代分裂方法与非线性求解器相结合具有显著优势——这类方法可松弛非线性项。最后，我们展望了多组分扩散方法后续研究方向的下一步探索。