Boundary layers and shock profiles for the discrete Boltzmann equation for mixtures

,Department Of Mathematics, Karlstad University, 651 88 Karlstad ,Niclas Bernhoff

doi:10.3934/krm.2012.5.1

,Department Of Mathematics, Karlstad University, 651 88 Karlstad , Niclas Bernhoff

Open Access

https://doi.org/10.3934/krm.2012.5.1

Copy DOI

Journal: Kinetic & Related Models	Publication Date: Jan 1, 2012
Citations: 36	License type: cc-by

Affiliation: Karlstad University

Abstract

We consider the discrete Boltzmann equation for binary gas mixtures. Some known results for half-space problems and shock profile solutions of the discrete Boltzmann for single-component gases are ...

Highlights

We consider the discrete Boltzmann equation (DBE) for twocomponent gases and extend some known results for single-component gases to this case
Half-space problems for the Boltzmann equation are of great importance in the study of the asymptotic behavior of the solutions of boundary value problems of the Boltzmann equation for small Knudsen numbers [28],[29]
Coworkers, has under a long time considered problems related to these questions, both from a theoretical and numerical point of view [28],[29]. Some of these results have been extended to the case of mixtures [31]

Summary

Introduction

We consider the discrete Boltzmann equation (DBE) for twocomponent gases and extend some known results for single-component gases to this case. Mathematical results for half-space problems for the Boltzmann equation for a single-component gas is reviewed in [3]. Coworkers, has under a long time considered problems related to these questions, both from a theoretical and numerical point of view [28],[29]. Some of these results have been extended to the case of mixtures [31]. Discrete velocity models, mixtures, half-space problems, boundary layers, shock profiles.

NICLAS BERNHOFF

MiB gjB

The Maxwellians are of the form

Then we obtain

We assume that

Assume that