Hermite spectral method for multi-species Boltzmann equation

TL;DR

This paper presents a Hermite spectral method for efficiently solving the multi-species Boltzmann equation, capable of handling up to 100 species with high accuracy and reduced computational cost.

Contribution

A novel Hermite spectral scheme with optimized collision models for multi-species Boltzmann equations, significantly improving efficiency and scalability.

Findings

Able to handle up to 100 species simultaneously

Demonstrates dramatic efficiency improvements over existing methods

Validates accuracy through numerical experiments

Abstract

We introduce a numerical scheme for the full multi-species Boltzmann equation based on Hermite spectral method. With the proper choice of expansion centers for different species, a practical algorithm is derived to evaluate the complicated multi-species binary collision operator. New collision models are built by combining the quadratic collision model and the simple BGK collision model under the framework of the Hermite spectral method, which enables us to balance the computational cost and accuracy. Several numerical experiments are implemented to validate the dramatic efficiency of this new Hermite spectral method. Moreover, we can handle the problems with as many as 100 species, which is far beyond the capability of the state-of-art algorithms.