Hermite spectral method for multi-species Boltzmann equation

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper presents a numerical scheme based on Hermite spectral method for solving the multi-species Boltzmann equation. By choosing proper expansion centers and collision models, a balance between computational cost and accuracy is achieved, and high-dimensional problems can be handled effectively.