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

Journal Article · Sat Aug 01 04:00:00 EDT 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01019701· OSTI ID:5267364

Fernandez-Feria, R; de la Mora, J F

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 error of order exp(-1/M), where M < 1 is the mass ratio. Comparison is made with results from a hypersonic approximation.

• Research Organization: Yale Univ., New Haven, CT (USA)
• OSTI ID: 5267364
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 48:3/4; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

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657002 -- Theoretical &amp; Mathematical Physics-- Classical &amp; Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCELERATION
BOLTZMANN EQUATION
BOLTZMANN STATISTICS
BROWNIAN MOVEMENT
CHARGED PARTICLES
COLLISIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
DISTRIBUTION FUNCTIONS
EQUATIONS
FLUIDS
FOKKER-PLANCK EQUATION
FUNCTIONS
GASES
HEAT FLUX
HELIUM IONS
IONIZED GASES
IONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SERIES EXPANSION
SHOCK WAVES
STATISTICAL MECHANICS
XENON IONS