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Resolving Knudsen layer by high-order moment expansion

  • Yuwei Fan
  • Jun Li
  • Ruo LiEmail author
  • Zhonghua Qiao
Original Article
  • 1 Downloads

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.

Keywords

Knudsen layer Kramers’ problem Hyperbolic moment equations Boltzmann equation 

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Notes

Acknowledgements

We thank the anonymous referees for their valuable comments and suggestions on the paper. The research of J. Li is partially supported by the Hong Kong Research Council ECS Grant No. 509213 during her visit periods at the Hong Kong Polytechnic University. The research of J. Li and R. Li is supported by the National Natural Science Foundation of China (11325102, 11421110001, 91630310). The research of Z.-H. Qiao is partially supported by the Hong Kong Research Council ECS Grant No. 509213 and the Hong Kong Polytechnic University research fund G-YBKP.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.School of Mathematical SciencesPeking UniversityBeijingChina
  3. 3.CAPT, LMAM & School of Mathematical SciencesPeking UniversityBeijingChina
  4. 4.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HomHong Kong

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