Advertisement

Keywords

Boltzmann Equation Euler Equation Kinetic Theory Hard Sphere Maxwell Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

1.10 Comments and bibliographic remarks

Section 1.1

  1. 36.
    L. Boltzmann. Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitzungsber. Akad. Wiss. Wien, 66:275–370, 1872.Google Scholar
  2. 49.
    C. Cercignani. Ludwig Boltzmann. The Man who Trusted Atoms. Oxford University Press, Oxford, 1998.Google Scholar

Section 1.2

  1. 82.
    K. Huang. Statistical mechanics. John Wiley & Sons Inc., New York, second edition, 1987.Google Scholar

Section 1.3

  1. 23.
    G. A. Bird. Monte-Carlo simulation in an engineering context. In S. Fisher, editor, Proc. of the 12th International Symposium on Rarefied Gas Dynamics (Charlottesville, 1980), volume 74 of Progress in Astronautics and Aeronautics, pages 239–255. AIAA, New York, 1981.Google Scholar
  2. 25.
    G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994.Google Scholar
  3. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. Sect. 2.4, 2.5Google Scholar
  4. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.71Google Scholar
  5. 60.
    M. H. Ernst. Exact solutions of the nonlinear Boltzmann and related kinetic equations. In Nonequilibrium phenomena. I. The Boltzmann equation, pages 51–119. North-Holland, 1983.Google Scholar
  6. 78.
    H. A. Hassan and D. B. Hash. A generalized hard-sphere model for Monte Carlo simulations. Phys. Fluids A, 5: 738–744, 1993.CrossRefGoogle Scholar
  7. 113.
    K. Koura and H. Matsumoto. Variable soft sphere molecular model for inversepower-law or Lennard-Jones potential. Phys. Fluids A, 3: 2459–2465, 1991.CrossRefGoogle Scholar
  8. 114.
    K. Koura and H. Matsumoto. Variable soft sphere molecular model for air species. Phys. Fluids A, 4: 1083–1085, 1992.CrossRefGoogle Scholar

Section 1.4

  1. 25.
    G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. Sect. 4.5Google Scholar
  2. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.118, Ref. 11Google Scholar
  3. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. Ch. IIIGoogle Scholar
  4. 51.
    C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. Ch. 8Google Scholar

Section 1.5

  1. 25.
    G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. p.91Google Scholar
  2. 25.
    G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. pp.25, 64, 82 165Google Scholar
  3. 40.
    G. Brasseur and S. Solomon. Aeronomy of the Middle Atmosphere. D. Reidel Publishing Company, Dordrecht, 1984.Google Scholar
  4. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.19Google Scholar
  5. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.233Google Scholar
  6. 131.
    M. J. McEwan and L. F. Phillips. The Chemistry of the Atmosphere. Edward Arnold (Publishers) Ltd., London, 1975.Google Scholar

Section 1.6

  1. 51.
    C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. p.36Google Scholar
  2. 51.
    C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. p.51Google Scholar
  3. 100.
    R. Kirsch. Die Boltzmann-Gleichung für energieabhängige Verteilungsfunktionen. Diplomarbeit, Universität des Saarlandes, 1999.Google Scholar

Section 1.7

  1. 25.
    G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. p.186Google Scholar
  2. 48.
    C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.85Google Scholar

Section 1.8

  1. 37.
    J.-F. Bourgat, P. Le Tallec, B. Perthame, and Y. Qiu. Coupling Boltzmann and Euler equations without overlapping. In Domain decomposition methods in science and engineering (Como, 1992), pages 377–398. Amer. Math. Soc., Providence, RI, 1994.Google Scholar
  2. 38.
    I. Boyd, G. Chen, and G. Candler. Predicting Failure of the Continuum Fluid Equations. AIAA, 94:2352, 1994.Google Scholar
  3. 74.
    M. Günther, P. Le Tallec, J. P. Perlat, and J. Struckmeier. Numerical modeling of gas flows in the transition between rarefied and continuum regimes. In Numerical flow simulation, I (Marseille, 1997), pages 222–241. Vieweg, Braunschweig, 1998.Google Scholar
  4. 101.
    A. Klar. Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations. Math. Methods Appl. Sci., 18(8):649–670, 1995.CrossRefGoogle Scholar
  5. 102.
    A. Klar. Domain decomposition for kinetic problems with nonequilibrium states. European J. Mech. B Fluids, 15(2):203–216, 1996.Google Scholar
  6. 103.
    A. Klar. Asymptotic analysis and coupling conditions for kinetic and hydrodynamic equations. Comput. Math. Appl., 35(1–2):127–137, 1998.CrossRefGoogle Scholar
  7. 117.
    P. Le Tallec and F. Mallinger. Coupling Boltzmann and Navier-Stokes equations by half fluxes. J. Comput. Phys., 136(1):51–67, 1997.CrossRefGoogle Scholar
  8. 123.
    H. W. Liepmann, R. Narasimha, and M. T. Chahine. Structure of a plane shock layer. Phys. Fluids, 5:1313, 1962.CrossRefGoogle Scholar
  9. 135.
    J. Meixner. Zur Thermodynamik irreversibler Prozesse. Z. Phys. Chem., 53B:253, 1941.Google Scholar
  10. 168.
    P. Quell. Nonlinear stability of entropy flux splitting schemes on bounded domains. IMA J. Numer. Anal., 20(3):441–459, 2000.CrossRefGoogle Scholar
  11. 199.
    S. Tiwari. Coupling of the Boltzmann and Euler equations with automatic domain decomposition. J. Comput. Phys., 144(2):710–726, 1998.CrossRefGoogle Scholar
  12. 200.
    S. Tiwari and A. Klar. An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. Appl. Math., 90(2):223–237, 1998.CrossRefGoogle Scholar
  13. 201.
    S. Tiwari and S. Rjasanow. Sobolev norm as a criterion of local thermal equilibrium. European J. Mech. B Fluids, 16(6):863–876, 1997.Google Scholar

Section 1.9

  1. 107.
    M. Knudsen. Kinetic Theory of Gases. Methuen, London, 1952.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Personalised recommendations