Journal of Statistical Physics

, Volume 1, Issue 4, pp 585–593 | Cite as

Velocity-space contours of collision integrals

  • R. Narasimha
  • S. M. Deshpande
  • P. V. Subba Raju
Note

Abstract

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

Key words

Kinetic theory of gases Boltzmann equation collision integrals nonequilibrium in hard-sphere gases numerical analysis of collision integrals exact results for collision integrals 

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References

  1. 1.
    R. Narasimha and S. M. Deshpande, “The Boltzmann collision integrals, I. General analysis,” Aeronautical Research Committee (India) ARC-TN-1 (1968).Google Scholar
  2. 2.
    S. M. Deshpande and R. Narasimha, “The Boltzmann collision integrals, II. Rigid spheres,” Aeronautical Research Committee (India) ARC-TN-2 (1969).Google Scholar
  3. 3.
    S. M. Deshpande and R. Narasimha, “The Boltzmann collision integrals for a combination of Maxwellians,”J. Fluid Mech. 36:545 (1969).Google Scholar
  4. 4.
    G. A. Bird, “The velocity distribution function within a shock wave,”J. Fluid Mech. 30:479 (1967).Google Scholar
  5. 5.
    A. Nordsieck and B. L. Hicks, “Monte Carlo evaluation of the Boltzmann collision integrals,”Proc. 5th Intl. Symp. on Rarefied Gas Dynamics, Oxford, Vol. 1, p. 695 (Academic Press, New York, 1967).Google Scholar
  6. 6.
    S. M. Yen and B. L. Hicks, “On the accuracy of approximate solutions of the Boltzmann equations,”Proc. 5th Intl. Symp. on Rarefied Gas Dynamics, Oxford, Vol. 1, p. 695 (Academic Press, New York, 1967).Google Scholar
  7. 7.
    B. L. Hicks and M. A. Smith, “Numerical studies of strong shock waves. Part X: On the accuracy of Monte Carlo solutions of the nonlinear Boltzmann equation,” Rep. R-360, Coordinated Science Laboratory, University of Illinois (1967).Google Scholar
  8. 8.
    A. Erdelyiet al., Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953).Google Scholar
  9. 9.
    R. Narasimha and S. M. Deshpande, “On the accuracy of Monte Carlo computations of the Boltzmann collision integrals,” Report 68 FM3, Department of Aeronautical Engineering, Indian Institute of Science, Bangalore, India (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • R. Narasimha
    • 1
  • S. M. Deshpande
    • 1
  • P. V. Subba Raju
    • 1
  1. 1.Department of Aeronautical EngineeringIndian Institute of ScienceBangaloreIndia

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