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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 2, Pages 329–343 (Mi zvmmf525)  

This article is cited in 61 scientific papers (total in 61 papers)

Solution to the Boltzmann kinetic equation for high-speed flows

F. G. Cheremisin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: The Boltzmann kinetic equation is solved by a finite-difference method on a fixed coordinate-velocity grid. The projection method is applied that was developed previously by the author for evaluating the Boltzmann collision integral. The method ensures that the mass, momentum, and energy conservation laws are strictly satisfied and that the collision integral vanishes in thermodynamic equilibrium. The last property prevents the emergence of the numerical error when the collision integral of the principal part of the solution is evaluated outside Knudsen layers or shock waves, which considerably improves the accuracy and efficiency of the method. The differential part is approximated by a second-order accurate explicit conservative scheme. The resulting system of difference equations is solved by applying symmetric splitting into collision relaxation and free molecular flow. The steady-state solution is found by the relaxation method.

Key words: Boltzmann kinetic equation, rarefied gas, numerical methods, high-speed flows.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:2, 315–329

Bibliographic databases:

UDC: 519.634
Received: 22.08.2003

Citation: F. G. Cheremisin, “Solution to the Boltzmann kinetic equation for high-speed flows”, Zh. Vychisl. Mat. Mat. Fiz., 46:2 (2006), 329–343; Comput. Math. Math. Phys., 46:2 (2006), 315–329

Citation in format AMSBIB
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    This publication is cited in the following articles:
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    6. Tcheremissine F.G., Agarwal R.K., “Computation of hypersonic shock waves in diatomic gases using the generalized Boltzmann equation”, Rarefied Gas Dynamics, AIP Conference Proceedings, 1084, 2009, 427–433  adsnasa  isi
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