Conservative semi-Lagrangian schemes for a general consistent BGK model for inert gas mixtures

TL;DR

This paper introduces high-order semi-Lagrangian schemes for a BGK model of inert gas mixtures, ensuring key physical properties and accurately capturing hydrodynamic limits through numerical simulations.

Contribution

It develops a novel high-order semi-Lagrangian scheme that preserves indifferentiability and asymptotic properties for a general BGK model of inert gas mixtures.

Findings

Scheme successfully preserves indifferentiability principle.

Scheme demonstrates asymptotic preserving property in simulations.

Accurately captures hydrodynamic limit behaviors.

Abstract

In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property, which allows us to capture the behaviors of hydrodynamic limit models. We consider two hydrodynamic closure which can be derived from the BGK model at leading order: classical Euler equations for number densities, global velocity and temperature, and a multi-velocities and temperatures Euler system. Numerical simulations are performed to demonstrate indifferentiability principle and asymptotic preserving property of the proposed conservative semi-Lagrangian scheme to the Euler limits.