Hermite spectral method for the inelastic Boltzmann equation
Numerical Analysis
2023-08-15 v2 Numerical Analysis
Abstract
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion coefficients for the VHS model are reduced into several summations and can be derived exactly. Moreover, a new collision model is built with a combination of the quadratic collision operator and a linearized collision operator, which helps us to balance the computational cost and the accuracy. Various numerical experiments, including spatially two-dimensional simulations, demonstrate the accuracy and efficiency of this numerical scheme.
Cite
@article{arxiv.2301.05850,
title = {Hermite spectral method for the inelastic Boltzmann equation},
author = {Ruo Li and Yixiao Lu and Yanli Wang},
journal= {arXiv preprint arXiv:2301.05850},
year = {2023}
}