Journal of Statistical Physics

, Volume 48, Issue 3–4, pp 901–917 | Cite as

Solution of the Fokker-Planck equation for the shock wave problem

  • R. Fernandez-Feria
  • J. Fernandez de la Mora
Articles

Abstract

An eigenexpansion solution of the time-independent Brownian motion Fokker-Planck equation is given for a situation in which the external acceleration is a step function. The solution describes the heavy-species velocity distribution function in a binary mixture undergoing a shock wave, in the limit of high dilution of the heavy species and negligible width of the light-gas internal shock. The diffusion solution is part of the eigenexpansion. The coefficients of the series of eigenfunctions are obtained analytically with transcendentally small errors of order exp(−1/M), whereM ≪ 1 is the mass ratio. Comparison is made with results from a hypersonic approximation.

Key words

Fokker-Planck equation shock wave Brownian motion eigentheory 

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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • R. Fernandez-Feria
    • 1
  • J. Fernandez de la Mora
    • 1
  1. 1.Department of Mechanical EngineeringYale UniversityNew Haven

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