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The Boltzmann collision integrals for a combination of Maxwellians

Published online by Cambridge University Press:  29 March 2006

S. M. Deshpande
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore 12
R. Narasimha
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore 12

Abstract

The gain and loss integrals in the Boltzmann equation for a rigid sphere gas are evaluated in closed form for a distribution which can be expressed as a linear combination of Maxwellians. Application to the Mott-Smith bimodal distribution shows that the gain is also bimodal, but the two modes in the gain are less pronounced than in the distribution. Implications of these results for simple collision models in non-equilibrium flow are discussed.

Type
Research Article
Copyright
© 1969 Cambridge University Press

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References

Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 Phys. Rev. 94, 511.
Chapman, S. & Cowling, T. G. 1960 The Mathematical Theory of Non-uniform gases. Cambridge University Press.
Deshpande, S. M. & Narasimha, R. 1969 Aero. Res. Comm. Tech. Note 2.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions. New York: McGraw-Hill.
Liepmann, H. W., Narasimha, R. & Chahine, M. T. 1962 Phys. Fluids. 5, 1313.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
Mott-Smith, H. M. 1951 Phys. Rev. 82, 885.
Narasimha, R. & Deshpande, S. M. 1968 Aero. Res. Comm. Tech. Note 1.
Narasimha, R. & Deshpande, S. M. 1969 J. Fluid Mech. 36, 555.
Slater, L. J. 1960 Confluent Hypergeometric Functions. Cambridge University Press.
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