High-order conservative asymptotic-preserving schemes for modeling rarefied gas dynamical flows with boltzmann-BGK equation

Manuel A. Diaz, Min-Hung Chen, Jaw Yen Yang

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1012-1049
Number of pages38
JournalCommunications in Computational Physics
Volume18
Issue number4
DOIs
Publication statusPublished - 2015 Oct 15

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rarefied gases
preserving
gas flow
BGK model
quadratures
conservation
viscosity
formulations
operators
collisions
kinetics

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

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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.",
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High-order conservative asymptotic-preserving schemes for modeling rarefied gas dynamical flows with boltzmann-BGK equation. / Diaz, Manuel A.; Chen, Min-Hung; Yang, Jaw Yen.

In: Communications in Computational Physics, Vol. 18, No. 4, 15.10.2015, p. 1012-1049.

Research output: Contribution to journalArticle

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