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A nonlinear half-space problem in the kinetic theory of gases

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Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1048)

Abstract

The problem of the steady emission of a monatomic gas from a plane boundary into a half-space under finite pressure is considered. The use of a trimodal approximating distribution function and moments derived from the nonlinear Boltzmann equation leads to a four-moment system that can be solved exactly. The solution is naturally arrived at in two steps: First, an algebraic connection problem between the nonequilibrium gas state at the boundary and the external equilibrium state is solved. Then, the actual relaxation from the one state to the other is computed. For Maxwell molecules this latter problem has a particularly simple solution, but only for flow conditions such that the macroscopic gas velocity away from the boundary remains subsonic.

Keywords

  • Boltzmann Equation
  • Moment Equation
  • Collision Term
  • Knudsen Layer
  • Maxwell Molecule

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© 1984 Springer-Verlag

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Ytrehus, T. (1984). A nonlinear half-space problem in the kinetic theory of gases. In: Cercignani, C. (eds) Kinetic Theories and the Boltzmann Equation. Lecture Notes in Mathematics, vol 1048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071884

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  • DOI: https://doi.org/10.1007/BFb0071884

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12899-1

  • Online ISBN: 978-3-540-38777-0

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