A unified implicit scheme for kinetic model equations. Part I. Memory reduction technique

Songze Chen, Chuang Zhang, Lianhua Zhu, Zhaoli Guo

Research output: Contribution to journalArticle

16 Citations (Scopus)


A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed from given macroscopic variables. Based on this fact, we propose a technique to reconstruct distribution function at discrete level, and employ it to develop an implicit numerical method for kinetic equations. The new implicit method only stores the macroscopic quantities which appear in the collision term, and does not store the distribution functions. As a result, enormous memory requirement for solving kinetic equations is totally relieved. Several boundary conditions, such as, inlet, outlet and isothermal boundaries, are discussed. Some numerical tests demonstrate the validity and efficiency of the technique. The new implicit solver provides nearly identical solution as the explicit kinetic solver, while the memory requirement is on the same order as the Navier–Stokes solver.

Original languageEnglish
Pages (from-to)119-129
Number of pages11
JournalScience Bulletin
Issue number2
Early online date29 Dec 2016
Publication statusPublished - 30 Jan 2017


  • implicit scheme
  • kinetic equation
  • memory reduction

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