Numerical Regularized Moment Method for High Mach Number Flow

TL;DR

This paper introduces a regularization technique for the numerical regularized moment method to improve the computation of shock waves at high Mach numbers, enhancing stability and accuracy.

Contribution

It develops a Maxwell iteration-based regularization approach for high-order moment systems, simplifying numerical implementation and extending applicability to high Mach number flows.

Findings

Successful computation of shock structures at high Mach numbers

Enhanced stability of the moment method with regularization

Validation through numerical experiments with various moments and Mach numbers

Abstract

This paper is a continuation of our earlier work \cite{NRxx} in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave with Mach number $M_0 \geqslant 3$. In this paper, we concentrate on the regularization of the moment systems. First, we apply the Maxwell iteration to the infinite moment system and determine the magnitude of each moment with respect to the Knudsen number. After that, we obtain the approximation of high order moments and close the moment systems by dropping some high-order terms. Linearization is then performed to obtain a very simple regularization term, thus it is very convenient for numerical implementation. To validate the new regularization, the shock structure of low order systems is computed with different number of moments and different shock Mach numbers.