Abstract
A recently developed accelerated deterministic method of approximation of the Boltzmann collision operator is applied in numerical modelling of the process of shock wave focusing in a rarefied noble gas. The results are compared with the results obtained previously for the same problem with the Boltzmann collision operator evaluated by the Monte Carlo quadrature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V.V. Aristov and F.G. Tcheremissine, Direct numerical solutions of the kinetic Boltzmann equation, (Comp. Center of Russ. Acad, of Sci., Moscow, 1992).
C. Buet, A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics, Trans. Theory Stat. Phys. 25, 33–60 (1996).
C. Cercignani, The Boltzmann Equation and its Applications, (Springer, 1988).
H. Grönig, Shock Wave Focusing Phenomena, In: 15th Shock Waves and Shock Tubes, Bershader and Hanson (Eds.), pp. 43–56 (Stanford University Press, Stanford, 1986).
P. Kowalczyk, T. Platkowski, and W. Walus, Focusing of a Shock Wave in a Rarefied Gas: A Numerical Study, Shock Waves, submitted, (1999).
T. Platkowski and W. Walus, An Acceleration Procedure for Discrete Velocity Approximation of the Boltzmann Collision Operator, accepted, Computers and Mathematics with Applications, (1999).
Z. Walenta, Focusing a shock wave: Microscopic structure of the phenomenon, Arch. Mech. 50, (1998).
F.G. Tcheremissine, Conservative evaluation of Boltzmann collision integral in discrete ordinates approximation, Comput. Math. Appl. 35, 215–221 (1998).
A. Palczewski, J. Schneider, and A.V. Bobylev, A consistency result for discrete -velocity model of the Boltzmann equation, SIAMJ. Numer. Anal. 34, 1865–1883 (1997).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kowalczyk, P., Platkowski, T., Waluś, W. (2000). Application of a Deterministic Scheme for the Boltzmann Equation in Modelling Shock Wave Focusing. In: Helbing, D., Herrmann, H.J., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’99. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59751-0_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-59751-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64109-1
Online ISBN: 978-3-642-59751-0
eBook Packages: Springer Book Archive