Hermite spectral method for the inelastic Boltzmann equation

Abstract

We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. This new approach involves utilizing a Hermite expansion, whereby the expansion coefficients for the variable hard sphere model are simplified into a series of summations that can be precisely derived. Additionally, a new collision model is built with a combination of the quadratic collision operator and a simplified 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.