Journal of Statistical Physics

, Volume 80, Issue 5–6, pp 1033–1061 | Cite as

A numerical method for computing asymptotic states and outgoing distributions for kinetic linear half-space problems

  • François Golse
  • Axel Klar


Linear half-space problems can be used to solve domain decomposition problems between Boltzmann and aerodynamic equations. A new fast numerical method computing the asymptotic states and outgoing distributions for a linearized BGK half-space problem is presented. Relations with the so-called variational methods are discussed. In particular, we stress the connection between these methods and Chapman-Enskog type expansions.

Key Words

Domain decomposition kinetic linear half-space problem variational methods 


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  1. 1.
    K. Aoki and Y. Sone, Gas flows around the condensed phase with strong evaporation or condensation, inAdvances in Kinetic Theory and Continuum Mechanics (Proceedings of a Symposium in Honor of H. Cabannes), R. Gatigol and Soubaramayer, eds. (Springer, 1991).Google Scholar
  2. 2.
    M. D. Arthur and C. Cercignani, Nonexistence of a steady rarefied supersonic flow in a half space,Z. Angew. Math. Phys. 31:634 (1980).Google Scholar
  3. 3.
    J. F. Bourgat, P. Le Tallec, D. Tidriri, and Y. Qiu, Numerical coupling of nonconservative or kinetic models with the conservative compressible Navier-Stokes equations, inFifth International Symposium on Domain Decomposition methods for P.D.E. (SIAM, Philadelphia, 1991).Google Scholar
  4. 4.
    C. Cercignani, A variational principle for boundary value problems,J. Stat. Phys. 1(2):297 (1969).Google Scholar
  5. 5.
    C. Cercignani, inMathematical Problems in the Kinetic Theory of Gases, D. C. Pack and H. Neunzert, eds. (Lang, Frankfurt, 1980), p. 129.Google Scholar
  6. 6.
    C. Cercignani,The Boltzmann Equation and its Applications (Springer, 1988).Google Scholar
  7. 7.
    F. Coron, Computation of the asymptotic states for linear half-space problems,Transport Theory Stat. Phys. 19(2):89 (1990).Google Scholar
  8. 8.
    F. Coron, F. Golse, and C. Sulem, A classification of well-posed kinetic layer problems,CPAM 41:409 (1988).Google Scholar
  9. 9.
    F. Golse, Applications of the Boltzmann equation within the context of upper atmosphere vehicle aerodynamcis,Comp. Meth. Eng. Appl. Mech. 75:299 (1989).Google Scholar
  10. 10.
    F. Golse, Knudsen layers from a computational viewpoint,Transport Theory Stat. Phys. 21(3):211 (1992).Google Scholar
  11. 11.
    W. Greenberg, C. van der Mee, and V. Protopopescu,Boundary Value Problems in Abstract Kinetic Theory (Birkhäuser, 1987).Google Scholar
  12. 12.
    R. Illner and H. Neunzert, Domain decomposition: Linking kinetic and aerodynamic descriptions, AGTM preprint 90, Kaiserlautern (1993).Google Scholar
  13. 13.
    H. G. Kaper, A Constructive approach to the solution of a class of boundary value problem of mixed type,J. Math. Anal. Appl. 63:691 (1978).Google Scholar
  14. 14.
    A. Klar, Domain decomposition for kinetic and aerodynamic equations, Ph.d. thesis, Kaiserslautern (1994).Google Scholar
  15. 15.
    S. K. Loyalka and J. H. Ferziger, Model dependence of the slip coefficient,Phys. Fluids 10(8):1833 (1967).Google Scholar
  16. 16.
    S. K. Loyalka, Approximate method in the kinetic theory,Phys. Fluids 11(14):2291 (1971).Google Scholar
  17. 17.
    A. Lukschin, H. Neunzert, and J. Struckmeier, Interim Report for the Hermes Project DPH 6174/91 (1992).Google Scholar
  18. 18.
    J. C. Maxwell,Phil. Trans. R. Soc. I (Appendix) (1879); reprinted inThe Scientific Papers of J. C. Maxwell (Dover, New York, 1965).Google Scholar
  19. 19.
    E. Ringeisen, Ph.d. thesis, Paris VII, (1992).Google Scholar
  20. 20.
    C. E. Siewert and J. R. Thomas, Strong evaporation into a half-space I,Z. Angew. Math. Phys. 32:421 (1981).Google Scholar
  21. 21.
    C. E. Siewert and J. R. Tomas, Strong evaporation into a half space II,Z. Angew. Math. Phys. 33:202 (1982).Google Scholar
  22. 22.
    Y. Sone and Y. Onishi, Kinetic theory of evaporation and condensation, hydrodynamic equation and slip boundary condition,J. Phys. Soc. Jpn. 44(6):1981 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • François Golse
    • 1
  • Axel Klar
    • 2
  1. 1.Denis Diderot, U.F.R. de MathématiquesUniversité Paris 7Paris Cedex 05
  2. 2.Fachbereich MathematikUniversität KaiserslauternKaiserslautern

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