Hermite spectral method for the inelastic Boltzmann equation

TL;DR

This paper introduces a Hermite spectral method for efficiently solving the inelastic Boltzmann equation, enabling accurate two-dimensional simulations by reducing computational complexity and balancing cost with precision.

Contribution

The paper presents a novel Hermite spectral algorithm with an innovative collision model for the inelastic Boltzmann equation, improving computational efficiency and accuracy.

Findings

Demonstrates high accuracy in 2D simulations

Achieves computational efficiency suitable for modern hardware

Balances cost and precision with a new collision model

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.