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SECTION B

Method of calculating the collision integral and solution of the Boltzmann kinetic equation for simple gases, gas mixtures and gases with rotational degrees of freedom

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Pages 1775-1789 | Received 16 Aug 2013, Accepted 23 Mar 2014, Published online: 28 May 2014

References

  • H. Alsmeyer, Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam, J. Fluid. Mech. 74 (1976), pp. 497–513. doi: 10.1017/S0022112076001912
  • Yu.A. Anikin, E.P. Derbakova, O.I. Dodulad, Yu.Yu. Kloss, D.V. Martynov, O.A. Rogozin, P.V. Shuvalov, and F.G. Tcheremissine, Computing of gas flows in micro- and nano-scale channels on the base of the Boltzmann Kinetic equation, Proc. Comput. Sci. 1(1) (2010), pp. 735–744. doi: 10.1016/j.procs.2010.04.079
  • Yu. A. Anikin, O.I. Dodulad, Yu.Yu. Kloss, D.V. Martynov, P.V. Shuvalov, and F.G. Tcheremissine, Development of applied software for analysis of gas flows in vacuum devices, Vacuum 86(11) (2012), pp. 1770–1777. doi: 10.1016/j.vacuum.2012.02.024
  • Yu.A. Anikin and O.I. Dodulad, Solution of a kinetic equation for diatomic gas with the use of differential scattering cross sections computed by the method of classical trajectories, Comput. Math. Math. Phys. 53(7) (2013), pp. 1193–1212. doi: 10.1134/S096554251307004X
  • R.M. Berns and A. van der Avoird, N2-N2 interaction potential from ab initio calculations, with application to the structure of (N2), J. Chem. Phys. 72 (1980), pp. 6107–6115. doi: 10.1063/1.439067
  • A.E. Beylich, An interlaced system for nitrogen gas, Technisch Hochcshule Report, Aachen, 2000.
  • A. Beylich, Solving the kinetic equation for all Knudsen numbers, Phys. Fluids 12(2) (2000), pp. 444–465. doi: 10.1063/1.870322
  • P.L. Bhatnagar, E.P. Gross, and M.A. Krook, Model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev. Online Arch. 94(3) (1954), pp. 511–525.
  • G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 2nd ed., Oxford University Press, New York, 1994.
  • F.G. Cheremisin, Conservative method of calculating the Boltzmann collision integral, Dokl. Phys. 42 (1997), pp. 607–610.
  • F.G. Cheremisin, Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime, Dokl. Phys. 45(8) (2000), pp. 401–404. doi: 10.1134/1.1310733
  • O.I. Dodulad and F.G. Tcheremissine, Multipoint conservative projection method for computing the Boltzmann collision integral for gas mixtures, 28th International Symposium on Rarefied Gas Dynamics, AIP Conf. Proc., Vol. 1501, 2012, pp. 302–309.
  • O.I. Dodulad and F.G. Tcheremissine, Computation of a shock wave structure in monatomic gas with accuracy control, Zh. Vychisl. Mat. Mat. Fiz. 53(6) (2013), pp. 1008–1026.
  • I.M. Gamba and Sri H. Tharkabhushanam, Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states, J. Comput. Phys. 228(6) (2009), 2012–2036. doi: 10.1016/j.jcp.2008.09.033
  • I.M. Gamba and S.H. Tharkabhushanam, Shock and boundary structure formation by spectral-Lagrangian methods for the inhomogeneous Boltzmann transport equation, J. Comput. Math. 28(4) (2010), pp. 430–460.
  • A.S. Gmurczyk, M. Tarczynski, and Z.A. Walenta, Shock wave structure in the binary mixtures of gases with disparate molecular masses, 11th International Symposium on Rarefied Gas Dynamics, Vol. 1, 1978, pp. 333–341.
  • J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids, University of Wisconsin, Wiley, 1964.
  • I. Ibragimov and S. Rjasanow, Numerical solution of the Boltzmann equation on the uniform grid, Computing 69(2) (2002), pp. 163–186. doi: 10.1007/s00607-002-1458-9
  • N.I. Khokhlov, Yu.Yu. Kloss, B.A. Shurygin, and F.G. Tcheremissine, Simulation of the temperature driven micro pump by solving the Boltzmann kinetic equation, Proceedings of the 26th International Symposium on Rarefied Gas Dynamics. AIP Conf. Proc., Vol. 1084, 2008, pp. 1039–1044. doi: 10.1063/1.3076435
  • N.M. Korobov, Approximate evaluation of multiple integrals, Dokl. Akad. Nauk SSSR. 124 (1959), pp. 1207–1210.
  • S. Kosuge, K. Aoki, and S. Takata, Shock-wave structure for a binary gas mixture: finite-difference analysis of the Boltzmann equation for hard-sphere molecules, Eur. J. Mech. B/Fluids 20(1) (2001), pp. 87–126. doi: 10.1016/S0997-7546(00)00133-3
  • K. Koura, Monte Carlo direct simulation of rotational relaxation of diatomic molecules using classical trajectory calculations: Nitrogen shock wave, Phys. Fluids 9(11) (1997), pp. 3542–3549. doi: 10.1063/1.869462
  • A.B. Morris, P.L. Varghese, and D.B. Goldstein, Monte Carlo solution of the Boltzmann equation via a discrete velocity model, J. Comput. Phys. 230 (2011), pp. 1265–1280. doi: 10.1016/j.jcp.2010.10.037
  • C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator, Math. Comput. 75 (2006), pp. 1833–1852. doi: 10.1090/S0025-5718-06-01874-6
  • T. Ohwada, Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules, Phys. Fluids, A Fluid Dyn. 5(1) (1993), pp. 217–234. doi: 10.1063/1.858777
  • T. Ohwada, Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite-difference analysis of the nonlinear Boltzmann equation for hard-sphere molecules, Phys. Fluids 8 (1996), pp. 2153–2160. doi: 10.1063/1.868989
  • A. Palczewski, J. Schneider, and A.V. Bobylev, Consistency result for a discrete-velocity model of the Boltzmann equation. l, SIAM J. Numer. Anal. 34(5) (1997), pp. 1865–1883. doi: 10.1137/S0036142995289007
  • P.J. Prince and J.R. Dormand, High order embedded Runge-Kutta formulae, J. Comput. Appl. Math. 67(7) (1981), pp. 67–75. doi: 10.1016/0771-050X(81)90010-3
  • A.A. Raines, Numerical solution of one-dimensional problems in binary gas mixture on the basis of the Boltzmann Equation, AIP Conf. Proc. 663(1) (2003), pp. 67–76. doi: 10.1063/1.1581527
  • F. Sharipov and J.L. Strapasson, Ab initio simulation of transport phenomena in rarefied gases, Phys. Rev. E 86 (2012), p. 031130. doi: 10.1103/PhysRevE.86.031130
  • F.G. Tcheremissine, Solution to the Boltzmann kinetic equation for high-speed flows, Comput. Math. Math. Phys. 46(2) (2006), pp. 315–329. doi: 10.1134/S0965542506020138
  • F.G. Tcheremissine, Method for solving the Boltzmann kinetic equation for polyatomic gases, Comput. Math. Math. Phys. 52(2) (2012), pp. 252–268. doi: 10.1134/S0965542512020054
  • W.P. Teagan and G.S. Springer, Heat-transfer and density-distribution measurements between parallel plates in the transition regime, Phys. Fluids 11(497) (1968), pp. 497–506. doi: 10.1063/1.1691944

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