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    Orlov, Alexander V. 1992. Extension of the Mott-Smith method to denser gases. Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue. 8, p. 1856.

    Orlov, A.V. 1992. Transport phenomena in a weak shock wave. Physica A: Statistical Mechanics and its Applications, Vol. 190, Issue. 3-4, p. 405.

    Hosokawa, Iwao 1988. Nonexistence of Any Exact Bimodal Solution for the Shock Wave Structure atM=∞. Journal of the Physical Society of Japan, Vol. 57, Issue. 6, p. 1865.

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    Eason, Ernest D. 1976. A review of least-squares methods for solving partial differential equations. International Journal for Numerical Methods in Engineering, Vol. 10, Issue. 5, p. 1021.

    Murthy, M.Krishna and Ramachandra, S.M. 1975. Ionizing shock waves in monatomic gases through a kinetic theory approach. Acta Astronautica, Vol. 2, Issue. 5-6, p. 367.

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    TAKATA, G. Y. and VOGENITZ, F. W. 1971. Rarefied hypersonic flow about cones and flat plates by Monte Carlo simulation. AIAA Journal, Vol. 9, Issue. 1, p. 94.

    Deshpande, S. M. and Narasimha, R. 1969. The Boltzmann collision integrals for a combination of Maxwellians. Journal of Fluid Mechanics, Vol. 36, Issue. 03, p. 545.


Minimum error solutions of the Boltzmann equation for shock structure

  • R. Narasimha (a1) and S. M. Deshpande (a1)
  • DOI:
  • Published online: 01 March 2006

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

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Journal of Fluid Mechanics
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