Communications in Mathematical Sciences

Volume 20 (2022)

Number 3

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

Pages: 695 – 725

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n3.a4

Authors

Seung Yeon Cho (Department of Mathematics and Computer Science, University of Catania, Italy; and Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju, South Korea)

Sebastiano Boscarino (Department of Mathematics and Computer Science, University of Catania, Italy)

Maria Groppi (Department of Mathematical, Physical and Computer Sciences, University of Parma, Italy)

Giovanni Russo (Department of Mathematics and Computer Science, University of Catania, Italy)

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 closures 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.

Keywords

BGK models for gas mixtures, semi-Lagrangian methods, high order numerical schemes

2010 Mathematics Subject Classification

65L06, 65M25, 76P05

Received 7 December 2020

Received revised 10 August 2021

Accepted 26 August 2021

Published 21 March 2022