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Tytuł artykułu

Kinetic boundary layers for the Boltzmann equation on discrete velocity lattices

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider families of discrete velocity models with physical collision invariants, and develop algebraic criteria for well-posedness of the linearized kinetic boundary layer problem. Using the obtained criteria we discuss various hierarchies of symmetric discrete velocity models, and calculate analytical and numerical slip coefficients for the representants of the hierarchies.
Rocznik
Strony
87--116
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Institute for Mathematics, Technical University of Ilmenau, Weimarer Str. 25, D-98693, Ilmenau, Germany
Bibliografia
  • 1. P. ROSTAND, Kinetic Boundary Layers, Numerical Simulations, J. Comp. Phys., 86, 18-55, 1990.
  • 2. C. CERCIGNANI, Theory and Applications of the Boltzmann Equation, Springer-Verlag, 1988.
  • 3. F. ROGIER and J. SCHNEIDER, A direct method for solving the Boltzmann equation, Transp. Theory Stat. Phys., 23, 313-338, 1994.
  • 4. P. BUET, A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics, Transp. Theory Stat. Phys., 25, 33-60, 1996.
  • 5. F.G. TCHEREMISSINE, Conservative Evaluation of the Boltzmann Collision Integral in Discrete Ordinate Approximation, Computer Math. Applic. 35, 1/2, 215-221, 1998.
  • 6. A, PALCZEWSKI, J. SCHNEIDER, A.V, BOBYLEV, A consistency result for discrete-velocity model of the Boltzrnann equation, SIAM J. Nunier. Anal. 34, 1997.
  • 7. A. PALCZEWSKI, J. SCHNEIDER, Existence, Stability and convergence of solutions of discrete velocity models to the Boltzmann Equation, J. Stat. Phys., 91, 1/2, 307-326, 1998.
  • 8. H. BABOVSKY, A constructive approach to steady nonlinear kinetic equations, Journ. of Comp. Appl. Mathematics, 89, 199-211, 1998.
  • 9. D.GoERSCH, Generalized Discrete Velocity Models, Math. Models and Methods in Appl. Sci., 12, 1, 49-76, 2002.
  • 10. T. PLATKOWSKI, W. WALUS, An Acceleration Procedure for Discrete Velocity Approximation of the Boltzmann Collision Operator, Computers and Mathematics with Applications, 39, 151-163, 2000.
  • 11. T. PLATKOWSKI and R. ILLNER, Discrete velocity models of the Boltzmann equation: A survey on the mathematical aspects of the theory, SIAM Review, 30, 213-255, 1998.
  • 12. A. A. BOBYLEV., C. CERCIGNANI, Discrete Velocity Models Without Non-physical Invariants, Journ. Stat. Phys., 97, 677-686, 1999.
  • 13. F. GOLSE, B. PERTHAME, C. SULEM, On a boundary layer problem for the nonlinear Boltzmann equation, Arch. Rational Mech. Anal., 103, 81-96, 1988.
  • 14. H. BABOVSKY, Kinetic boundary layers: on the adequate discretization of the Boltzmann collision operator, Journ. of Comp. Appl. Mathematics, 110, 225-239, 1999.
  • 15. H. BABOVSKY and P. KOWALCZYK, Diffusion limits for discrete velocity models in a thin gap, Multiscale Modelling and Simulation, 6, 631-655, 2007.
  • 16. L. S. ANDALLAH, H. BABOVSKY, A discrete Boltzmann equation based on hexagons, Math. Models Methods Appl. Sci., 13, 1537-1563, 2003.
  • 17. H. BABOVSKY, A numerical scheme for the Boltzmann equation, Proceedings of the 25th Int. Symposium on RGD, M.S. IVANOV and A. K. REBROV [Eds.], 268-273, Novosibirsk 2007.
  • 18. C. BARDOS, R. CAFLISCH and B. NICOLAENKO, The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas, Comm. Pure Appl. Math., 39, 323-352, 1986.
  • 19. A. A. BOBYLEV, C. CERCIGNANI, Discrete Velocity Models for Mixtures, Journ. Stat. Phys., 91, 327-342, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0012-0025
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