Abstract
One of the major shortcomings in dealing with the Boltzmann equation is the complicated nature of the collision integral, in both the full nonlinear version, Eq. (1.1) of Chapter II, and the linearized form, Eq. (2.2) of Chapter III. It is therefore not surprising that alternative, simpler expressions have been proposed for the collision term; they are known as collision models, and any Boltzmann-like equation where the Boltzmann collision integral is replaced by a collision model is called a model equation or a kinetic model.
This is a preview of subscription content, log in via an institution to check access.
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
P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954);
P. Welander, Arkiv. Fysik. 7, 507 (1954);
M. Krook, J. Fluid Mech. 6, 523 (1959);
L. H. Holway, Jr., “Approximation Procedures for Kinetic Theory,” Ph.D. Thesis, Harvard University (1963)
C. Cercignani and G. Tironi, in: Rarefied Gas Dynamics (C. L. Brundin, ed.), Vol. I, p. 441, Academic Press, New York (1967).
E. P. Gross and E. A. Jackson, Phys. Fluids 2, 432 (1959);
L. Sirovich, Phys. Fluids 5, 908 (1962).
L. H. Holway, Jr., “Sound Propagation in a Rarefied Gas Calculated from Kinetic Theory by Means of a Statistical Model,” Raytheon Co. Report T-578 (1964);
C. Cercignani and G. Tironi, Nuovo Cimento 43, 64 (1966).
C. Cercignani, Ann. Phys. (N.Y.) 40, 469 (1966);
S. K. Loyalka and J. H. Ferziger, Phys. Fluids 10, 1833 (1967).
C. Cercignani, “Boundary Value Problems in Linearized Kinetic Theory,” in: Transport Theory (R. Bellman, G. Birkhoff, and I. Abu-Shumays, eds.), SIAM-AMS Proceedings, Vol. I, p. 249, American Mathematical Society, Providence (1968);
S. F. Shen, Entropie 18, 138 (1967).
E. P. Gross, E. A. Jackson, and S. Ziering, Ann. Phys. (N.Y.) 1, 141 (1957).
I. Kuščer, J. Mozina, and F. Krizanic, in: Rarefied Gas Dynamics (D. Dini, S. Nocilla, and C. Cercignani, eds.), Vol. I, p. 97, Editrice Tecnico-Scientifica, Pisa (1971).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cercignani, C. (1990). Model Equations. In: Mathematical Methods in Kinetic Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7291-0_4
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7291-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7293-4
Online ISBN: 978-1-4899-7291-0
eBook Packages: Springer Book Archive