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Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision

Published online by Cambridge University Press:  03 June 2015

Zhenning Cai ,
Yuwei Fan ,
Ruo Li  and
Zhonghua Qiao
Zhenning Cai*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
Yuwei Fan*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
Ruo Li*
Affiliation:
CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Zhonghua Qiao*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
*
Email:caizn@pku.edu.cn
Email:ywfan@pku.edu.cn
Email:rli@math.pku.edu.cn
Corresponding author.Email:zqiao@polyu.edu.hk
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Abstract

We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.

Keywords

35L2565M0876P0578M05Dimension-reductionmoment systemNRxxglobal hyperbolicityboundary conditionmicroflow
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1368 - 1406
Copyright
Copyright © Global Science Press Limited 2014

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