Resolving Knudsen layer by high-order moment expansion

Yuwei Fan; Jun Li; Ruo Li; Zhonghua Qiao

doi:10.1007/s00161-019-00749-3

Resolving Knudsen layer by high-order moment expansion

Yuwei Fan, Jun Li, Ruo Li, Zhonghua Qiao

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

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 language	English
Pages (from-to)	1313-1337
Number of pages	25
Journal	Continuum Mechanics and Thermodynamics
Volume	31
Issue number	5
DOIs	https://doi.org/10.1007/s00161-019-00749-3
Publication status	Published - 1 Sep 2019

Keywords

Boltzmann equation
Hyperbolic moment equations
Knudsen layer
Kramers’ problem

ASJC Scopus subject areas

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

More information

10.1007/s00161-019-00749-3

Cite this

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title = "Resolving Knudsen layer by high-order moment expansion",

abstract = "We model the Knudsen layer in Kramers{\textquoteright} 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{\textquoteright} 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.",

keywords = "Boltzmann equation, Hyperbolic moment equations, Knudsen layer, Kramers{\textquoteright} problem",

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AU - Fan, Yuwei

AU - Li, Jun

AU - Li, Ruo

AU - Qiao, Zhonghua

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Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Hyperbolic moment equations

KW - Knudsen layer

KW - Kramers’ problem

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SP - 1313

EP - 1337

JO - Continuum Mechanics and Thermodynamics

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SN - 0935-1175

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