Resolving Knudsen layer by high-order moment expansion

Yuwei Fan, Jun Li, Ruo Li, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review


We model the Knudsen layer in Kramers’ problem by the linearized high-order hyperbolic moment system. Thanks to the hyperbolicity of the moment system, its boundary conditions are properly reduced from the kinetic boundary condition. For the Kramers’ problem, we present the analytical solutions of the linearized moment systems. The velocity profile in the Knudsen layer is captured with improved accuracy for a wide range of accommodation coefficients. With the order of the moment system increasing, the velocity profile approaches to that of the linearized Boltzmann–BGK equation.

Original languageEnglish
Pages (from-to)1313-1337
Number of pages25
JournalContinuum Mechanics and Thermodynamics
Issue number5
Publication statusPublished - 1 Sep 2019


  • Boltzmann equation
  • Hyperbolic moment equations
  • Knudsen layer
  • Kramers’ problem

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

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