Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

TL;DR

This paper develops a numerical scheme for a multi-species BGK kinetic model with velocity-dependent collision frequency, ensuring conservation laws and positivity, and demonstrates its effectiveness through numerical tests.

Contribution

It introduces an IMEX-based numerical method for a generalized multi-species BGK model with velocity-dependent collision frequency, preserving key physical properties.

Findings

Conservation of mass, momentum, and energy is maintained.

Positivity of distribution functions is preserved.

Numerical examples demonstrate the method's effectiveness.

Abstract

We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure \cite{arXiv:2101.09047}. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.