An Efficient NRxx Method for Boltzmann-BGK Equation

TL;DR

This paper enhances the NRxx numerical regularized moment method for Boltzmann-BGK equations by integrating advanced techniques to improve efficiency and accuracy, validated through numerical experiments.

Contribution

It introduces combined techniques such as HLL flux, RKC schemes, and revised Strang splitting to significantly improve the efficiency of the NRxx method.

Findings

Overall efficiency is significantly improved.

Convergence order is maintained.

Numerical validation confirms effectiveness.

Abstract

In \cite{NRxx}, we proposed a numerical regularized moment method of arbitrary order (abbreviated as NRxx method) for Boltzmann-BGK equation, which makes numerical simulation using very large number of moments possible. In this paper, we are further exploring the efficiency of NRxx method with techniques including the 2nd order HLL flux with linear reconstruction to improve spatial accuracy, the RKC schemes to relieve the time step length constraint by the regularization terms, and the revised Strang splitting to calculate convective and diffusive terms only once without loss of accuracy. It is validated by the numerical results that the overall efficiency is significantly improved and the convergence order is kept well.