Abstract
One consider a method for solving the Boltzmann kinetic equation for a gas flow which is close to the local thermadynamic equilibrium. To eliminate the “stiffness” of the equation, a special method for evaluation of the collision integral is developed. The numerical algorithm uses the splitting on a relaxation and on a transport stages. The scheme for the relaxation stage is conservative and gives correct asymptotic solution when the time stepτ→∞. For the transport stage the conservative flux-corrected scheme is applied. Some examples of calculations are presented.
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References
Chapman S. and Cowling T., The Mathematical Theory of Non-uniform Gases, Cambridge University Press, Cambridge, U.K., (1952).
Kogan M.N.,Rarefied Gas Dynamics, Plenum Press, N.Y., (1969).
Beylich A.E.,Solving the Kinetic Equation for all Knudsen Numbers, Phys. Fluids, 12(12) (2000), 444–465.
Shi JinRunge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms, J. Comput. Phys., 122 (1995), 51–67.
Caflisch R., Jin S., Russo G., Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation, SIAM J. Numer.Anal., 34(1) (1997), 246–281.
Cheremisin F.G., Conservative Method of Evaluation of the Boltzmann Collision Integral, Physics ¡ª Doclady, 357(1) (1997), 53–56.
Tcheremissine F.G., Conservative Evaluation of Boltzmann Collision Integral in Discrete Ordinates Approximation, Computers. Math. Applic., 35(1–2) (1998), 215–221.
Aristov V.V., Tcheremissine F.G.,Splitting of the Non-Uniform Kinetic Operator of the Boltzmann Equation,Doklady AN USSR, 231(1) (1976), 49–52.
Aristov V.V., Tcheremissine F.G., The Kinetic Numerical Method for Rarefied and Continuum Gas Flows, Proc. 13-th Intern. Symp. on RGD, Plenum Press, N.Y., (1985), 269–276.
Boris J.P., Book D.L., Flux-Corrected Transport. 1.SHASTA,A Fluid Transport Algorithm That Works, Journal of Comp. Physics, 11 (1973), 38–69.
Korobov N.M., Trigonometric Sums and Their Applications, Mir, Moscow, (1989).
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© 2001 Springer Basel AG
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Tcheremissine, F.G. (2001). Solution of the Boltzmann Equation in Stiff Regime. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_42
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_42
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
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