Dimension-reduced hyperbolic momentmethod for the boltzmann equation with BGK-type collision

Zhenning Cai, Yuwei Fan, Ruo Li, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


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 highdimensional 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.
Original languageEnglish
Pages (from-to)1368-1406
Number of pages39
JournalCommunications in Computational Physics
Issue number5
Publication statusPublished - 1 Jan 2014


  • Boundary condition
  • Dimension-reduction
  • Global hyperbolicity
  • Microflow
  • Moment system
  • NRxx

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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