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High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation

Part of: Rarefied gas flows, Boltzmann equation Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  15 October 2015

Manuel A. Diaz ,
Min-Hung Chen  and
Jaw-Yen Yang
Manuel A. Diaz
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taiwan, Taipei 10167
Min-Hung Chen
Affiliation:
Department of Mathematics, National Cheng-Kung University, Taiwan, Tainan 701
Jaw-Yen Yang*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taiwan, Taipei 10167 Institute of Advanced Study in Theoretical Science, National Taiwan University, Taiwan, Taipei 10167
*
*Corresponding author. Email addresses: [email protected] (M. A. Diaz), [email protected] (M.-H. Chen), [email protected] (J.-Y. Yang)
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Abstract

High-order and conservative phase space direct solvers that preserve the Euler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gas flows are explored and studied. The approach is based on the conservative discrete ordinate method for velocity space by using Gauss Hermite or Simpsons quadrature rule and conservation of macroscopic properties are enforced on the BGK collision operator. High-order asymptotic-preserving time integration is adopted and the spatial evolution is performed by high-order schemes including a finite difference weighted essentially non-oscillatory method and correction procedure via reconstruction schemes. An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equation when the correction procedure via reconstruction scheme is used. The effects of the discrete velocity conservative property and accuracy of high-order formulations of kinetic schemes based on BGK model methods are provided. Extensive comparative tests with one-dimensional and two-dimensional problems in rarefied gas flows have been carried out to validate and illustrate the schemes presented. Potentially advantageous schemes in terms of stable large time step allowed and higher-order of accuracy are suggested.

Keywords

Rarefied gas dynamicsBoltzmann-BGK equationasymptotic preservingconservative discrete ordinate methodweighted essentially non-oscillatorycorrection procedure via reconstructionartificial viscosity

MSC classification

Secondary: 35Q20: Boltzmann equations 76P05: Rarefied gas flows, Boltzmann equation
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 1012 - 1049
Copyright
Copyright © Global-Science Press 2015 

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