High order asymptotic-preserving schemes for the Boltzmann equation

TL;DR

This paper develops high order asymptotic-preserving numerical schemes for the Boltzmann equation using IMEX Runge-Kutta methods combined with a penalization technique, enabling efficient simulations across different regimes.

Contribution

It introduces a novel combination of IMEX Runge-Kutta schemes with penalization for high order asymptotic-preserving discretization of the Boltzmann equation.

Findings

Successfully constructs high order schemes.

Demonstrates stability and accuracy across regimes.

Extends previous methods with improved order.

Abstract

In this note we discuss the construction of high order asymptotic preserving numerical schemes for the Boltzmann equation. The methods are based on the use of Implicit-Explicit (IMEX) Runge-Kutta methods combined with a penalization technique recently introduced in [F. Filbet, S. Jin: A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources,J. Comp. Phys. 229, (2010), pp. 7625-7648.].