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arXiv · 1806.09462

A consistent kinetic model for a two-component mixture with an application to plasma

Christian Klingenberg·Marlies Pirner·Gabriella Puppo
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Abstract

We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the solutions for the space homogeneous case, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the space homogeneous case in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. In particular, by considering a mixture composed of ions and electrons, we derive the macroscopic equations of ideal MHD from our model.

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Christian Klingenberg, Marlies Pirner, Gabriella Puppo. 2018-06-25. A consistent kinetic model for a two-component mixture with an application to plasma. https://doi.org/10.3934/krm.2017017

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