Commun. Comput. Phys., 11 (2012), pp. 1415-1438.


Numerical Regularized Moment Method for High Mach Number Flow

Zhenning Cai 1*, Ruo Li 2, Yanli Wang 1

1 School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
2 CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.

Received 5 January 2011; Accepted (in revised version) 14 July 2011
Available online 8 December 2011
doi:10.4208/cicp.050111.140711a

Abstract

This paper is a continuation of our earlier work [SIAM J. Sci. Comput., 32(2010), pp. 2875-2907] 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 $M_0 \geq 3$. 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 structures of low order systems are computed with different shock Mach numbers.

AMS subject classifications: 65M08, 65M12

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Key words: Boltzmann-BGK equation, Maxwellian iteration, regularized moment equations.

*Corresponding author.
Email: caizn@pku.edu.cn (Z. Cai), rli@math.pku.edu.cn (R. Li), wangyanliwyl@gmail.com (Y. Wang)
 

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