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1.10 Comments and bibliographic remarks
Section 1.1
L. Boltzmann. Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitzungsber. Akad. Wiss. Wien, 66:275–370, 1872.
C. Cercignani. Ludwig Boltzmann. The Man who Trusted Atoms. Oxford University Press, Oxford, 1998.
Section 1.2
K. Huang. Statistical mechanics. John Wiley & Sons Inc., New York, second edition, 1987.
Section 1.3
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.
G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994.
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. Sect. 2.4, 2.5
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.71
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.
H. A. Hassan and D. B. Hash. A generalized hard-sphere model for Monte Carlo simulations. Phys. Fluids A, 5: 738–744, 1993.
K. Koura and H. Matsumoto. Variable soft sphere molecular model for inversepower-law or Lennard-Jones potential. Phys. Fluids A, 3: 2459–2465, 1991.
K. Koura and H. Matsumoto. Variable soft sphere molecular model for air species. Phys. Fluids A, 4: 1083–1085, 1992.
Section 1.4
G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. Sect. 4.5
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.118, Ref. 11
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. Ch. III
C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. Ch. 8
Section 1.5
G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. p.91
G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. pp.25, 64, 82 165
G. Brasseur and S. Solomon. Aeronomy of the Middle Atmosphere. D. Reidel Publishing Company, Dordrecht, 1984.
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.19
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.233
M. J. McEwan and L. F. Phillips. The Chemistry of the Atmosphere. Edward Arnold (Publishers) Ltd., London, 1975.
Section 1.6
C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. p.36
C. Cercignani, R. Illner, and M. Pulvirenti. The Mathematical Theory of Dilute Gases. Springer, New York, 1994. p.51
R. Kirsch. Die Boltzmann-Gleichung für energieabhängige Verteilungsfunktionen. Diplomarbeit, Universität des Saarlandes, 1999.
Section 1.7
G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994. p.186
C. Cercignani. The Boltzmann Equation and its Applications. Springer, New York, 1988. p.85
Section 1.8
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.
I. Boyd, G. Chen, and G. Candler. Predicting Failure of the Continuum Fluid Equations. AIAA, 94:2352, 1994.
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.
A. Klar. Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations. Math. Methods Appl. Sci., 18(8):649–670, 1995.
A. Klar. Domain decomposition for kinetic problems with nonequilibrium states. European J. Mech. B Fluids, 15(2):203–216, 1996.
A. Klar. Asymptotic analysis and coupling conditions for kinetic and hydrodynamic equations. Comput. Math. Appl., 35(1–2):127–137, 1998.
P. Le Tallec and F. Mallinger. Coupling Boltzmann and Navier-Stokes equations by half fluxes. J. Comput. Phys., 136(1):51–67, 1997.
H. W. Liepmann, R. Narasimha, and M. T. Chahine. Structure of a plane shock layer. Phys. Fluids, 5:1313, 1962.
J. Meixner. Zur Thermodynamik irreversibler Prozesse. Z. Phys. Chem., 53B:253, 1941.
P. Quell. Nonlinear stability of entropy flux splitting schemes on bounded domains. IMA J. Numer. Anal., 20(3):441–459, 2000.
S. Tiwari. Coupling of the Boltzmann and Euler equations with automatic domain decomposition. J. Comput. Phys., 144(2):710–726, 1998.
S. Tiwari and A. Klar. An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. Appl. Math., 90(2):223–237, 1998.
S. Tiwari and S. Rjasanow. Sobolev norm as a criterion of local thermal equilibrium. European J. Mech. B Fluids, 16(6):863–876, 1997.
Section 1.9
M. Knudsen. Kinetic Theory of Gases. Methuen, London, 1952.
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(2005). Kinetic theory. In: Stochastic Numerics for the Boltzmann Equation. Springer Series in Computational Mathematics, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27689-0_1
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