Abstract
In the present Chapter we describe our approach concerning the discrete velocity technique which allows one to use, in fact, the deterministic integration in the collision operators [1–3]. Note, that the other discrete velocity approaches with constant coefficients in the quadratic form approximating the right-hand side of the Boltzmann equation are developed in recent years [4–6]. Such numerical schemes are attractive due to the simple structure of terms that approximate the collision integrals, good perspectives for paralleling, a clear way for estimating numerical errors, etc.
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References
Aristov V.V. (1985) Solving the Boltzmann equation for discrete velocities, Doklady Academii Nauk SSSR, Vol. no. 283, pp.831–834.
Aristov V.V. (1991) Development of the regular method of solution of the Boltzmann equation and nonuniform relaxation problems, Rarefied Gas Dynamics, ed. A. Beylich, VCH, Weinheim, pp.879–885.
Aristov V.V. (1992) Method of solving the Boltzmann equation by integration over collision parameters in piecewise-constant approximation, Modern problems in computational aerodynamics, A. Dorodnicyn, P. Chushkin eds., Mir Publishers, Moscow / CRC Press, Boca Raton, Ann Arbor, London, pp. 357–375.
Tan Z., Chen Y.-K., Varghese P.L., Howell J.R. (1989) A new numerical strategy to evaluate the collision integral of the Boltzmann equation, Rarefied Gas Dynamics, Progress in Astronaut. and Aeronaut., AIIA, Washington, Vol. no. 118, pp. 359–373.
Martin Y.-L., Rogier F., Schneider J. (1992) Une methode deterministe pour la resolution de l’equation de Boltzman inhomogene, C.R.Acad. Sci., Vol. no. 314, Serie 1, pp.483–487.
Tan Z., Varghese P.L. (1994) The Δ — ε method for the Boltzmann equation, J. Comp. Phys., Vol. no. 110, pp. 327–340.
Aristov V.V., Tcheremissine F.G. (1980) Conservative splitting method for solving the Boltzmann equation. USSR J. Comp. Maths. Math. Phys., Vol. no. 20, pp. 208–225.
Aristov V.V., Zabelok S.A. (1998) Parallel computing for the Boltzmann equation in deterministic integration, Communications on Applied Math., Computing Center of the Russian Acad. Sei., Moscow.
Aristov V.V., Zabelok S.A. (1998) Parallel algorithms in the conservative splitting method for the Boltzmann equation, Lecture Notes in Physics, Vol.515, pp. 361–366.
Rykov V.A. (1967) Relaxation of a gas described by the kinetic Boltzmann equation, Prikladnaia Matematica i Mechanica, Vol. no. 31, pp. 756–762
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Aristov, V.V. (2001). Deterministic (Regular) Method for Solving the Boltzmann Equation. In: Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Fluid Mechanics and its Applications, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0866-2_4
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DOI: https://doi.org/10.1007/978-94-010-0866-2_4
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