On steady-state preserving spectral methods for homogeneous Boltzmann equations

TL;DR

This paper introduces a spectral method for the homogeneous Boltzmann equation that exactly preserves Maxwellian steady-states and achieves spectral accuracy uniformly over time.

Contribution

It presents a novel spectral method that maintains the Maxwellian steady-state exactly, improving the accuracy and stability of solutions for the Boltzmann equation.

Findings

Exact preservation of Maxwellian steady-states

Spectral accuracy in approximating solutions

Uniform accuracy over time

Abstract

In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady-state of the system. We show that the resulting method is able to approximate with spectral accuracy the solution uniformly in time.