Numerical solution of the Boltzmann equation for the shock wave in a gas mixture

TL;DR

This paper presents a numerical method for solving the Boltzmann equation to analyze shock wave structures in multi-component gas mixtures, extending existing techniques and validating results against previous studies.

Contribution

The authors extend the Conservative Projection Method to gas mixtures in cylindrical coordinates for the first time, enabling detailed shock wave analysis.

Findings

Accurate shock wave profiles for multi-component gases obtained.

Good agreement with previous numerical and experimental data.

Demonstrated effectiveness of the extended method for complex gas mixtures.

Abstract

We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use the Conservative Projection Method developed by F.G. Tscheremissine which we extended to gas mixtures in cylindrical coordinates. The transition from the upstream to downstream uniform state is presented by macroscopic values and distribution functions. The obtained results were compared with numerical and experimental results of other authors.