Abstract
A previously constructed kinetic model for describing the behavior of a nonideal gas is investigated. The dimensionless parameters determining when the nonideal nature of the gas has to be taken into account are estimated in more detail. It is found that the collision integral for bound particles can be integrated over the velocity space, which significantly simplifies the original system of equations and makes it possible to prove an H-theorem. The resulting system is nondimensionalized. A conservative numerical scheme is proposed for its solution.
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REFERENCES
A. M. Bishaev and V. A. Rykov, “Construction of a system of kinetic equations for a nonideal gas,” High Temp. 55, 27–39 (2017).
D. V. Sivukhin, General Course of Physics, Vol. 2: Thermodynamics and Molecular Physics (Nauka, Moscow, 1975) [in Russian].
A. A. Vlasov, Nonlocal Statistical Mechanics (Nauka, Moscow, 1976) [in Russian].
A. M. Bishaev, V. A. Rykov, and M. V. Abgaryan, “The H-theorem and equation of state for kinetic model of imperfect gas,” J. Phys. Conf. Ser., 1–5 (2018).
F. G. Tcheremissine, “Solution to the Boltzmann kinetic equation for high-speed flows,” Comput. Math. Math. Phys. 46 (2), 315–329 (2006).
I. N. Larina and V. A. Rykov, “Numerical solution of the Boltzmann equation by a symmetric splitting method,” Comput. Math. Math. Phys. 43 (4), 575–586 (2003).
M. V. Abgaryan and A. M. Bishaev, “Modification of the splitting method as applied to a system of kinetic equations describing the behavior of a rarefied plasma jet,” Comput. Math. Math. Phys. 58 (7), 1081–1098 (2018).
M. N. Kogan, Rarefied Gas Dynamics (Nauka, Moscow, 1967; Plenum, New York, 1969).
V. Ya. Rudyak, Statistical Theory of Dissipative Processes in Gases and Liquids (Nauka, Moscow, 1987) [in Russian].
A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics: A Unified Introduction with Applications (Nauka, Moscow, 1987; Birkhäuser, Basel, 1987).
V. A. Titarev and E. M. Shakhov, “Numerical analysis of the spiral Couette flow of a rarefied gas between coaxial cylinders,” Comput. Math. Math. Phys. 46 (3), 505–513 (2006).
Funding
The article was prepared during the work on the grant “Development of methods of numerical modeling of engineering problems of rarefied gas mechanics” with unique number 18-08-00501.
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Translated by I. Ruzanova
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Abgaryan, M.V., Bishaev, A.M. & Rykov, V.A. Numerical Method for Solving a System of Kinetic Equations Describing the Behavior of a Nonideal Gas. Comput. Math. and Math. Phys. 60, 1488–1498 (2020). https://doi.org/10.1134/S096554252009002X
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DOI: https://doi.org/10.1134/S096554252009002X