Since the BGK model is based on the assumption of constant collision frequency, and since this model has been found inadequate in describing some experimental data, the numerical study of a variable collision frequency model proposed earlier by Cercignani and Loyalka and Ferziger is described. Specifically, the Kramer’s problem for this model is solved, and it is found that the ’’velocity defect’’ in the Knudsen layer is quite sensitive to the velocity dependence of the collision frequency. In fact, for the hard sphere collision frequency, the present results agree reasonably well with the recent experimental data of Reynolds, Smolderen, and Wendt.
REFERENCES
1.
2.
3.
S. K. Loyalka, Ph.D. thesis, Stanford University (1967);
4.
C. Cercignani, Mathematical Methods in Kinetic Theory (Plenum, New York, 1968).
5.
M. M. R. Williams, Mathematical Methods in Particle Transport Theory (Butterworths, London, 1971). See in particular, pp. 231 and 351.
6.
S. K.
Loyalka
, N.
Petrellis
, and T. S.
Storvick
, Phys. Fluids
18
, 1094
(1975
).7.
M. A. Reynolds, J. J. Smolderen, and J. F. Wendt, in Rarefied Gas Dynamics, edited by M. Befker and M. Fiebig (DFVLR‐Press, Proz Wahn, Germany, 1974), Vol. I, p. A‐21.
8.
W. Rixen and G. Adomeit, in Rarefied Gas Dynamics, edited by M. Becker and M. Fiebig (DFVLR‐Press, Porz Wahn, Germany, 1974), Vol. I, p. 8–18.
9.
S. K. Loyalka, in Rarefied Gas Dynamics, edited by M. Becker and M. Fiebig (DFVLR‐Press, Porz Wahn, Germany, 1974), Vol. I, p. A‐5.
10.
11.
G. A. Kronrod, Nodes and Weights for Quadrature Formula (Consultants Bureau, New York, 1965).
12.
J. F. Wendt (private communication).
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© 1975 American Institute of Physics.
1975
American Institute of Physics
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