The steady flow of a rarefied gas past an almost specularly reflecting plate is considered. Because of the assumptions the Boltzmann equation can be linearized about a streaming Maxwellian provided that alpha VM LS TH 1 and alpha M VM LS TH 1, where alpha and M are the accommodation coefficient at the plate surface and the Mach number respectively. The collisions in the linearized kinetic equation are described by the BGK model. The resulting equation is Fourier transformed, and a linear system involving the unknown Fourier transformed density, velocity and temperature perturbations is obtained. It is shown that the calculation of the coefficients of the system can be reduced to the evaluation of only two one-dimensional integrals, one of which is essentially the plasma dispersion function. This circumstance is particularly relevant for the numerical computation of the Fourier transforms and its inversion.

HIGH MACH NUMBER FLOW OF A RAREFIED GAS PAST AN ALMOST SPECULARLY REFLECTING PLATE.

CERCIGNANI, CARLO;FREZZOTTI, ALDO;LAMPIS, MARIA
1985

Abstract

The steady flow of a rarefied gas past an almost specularly reflecting plate is considered. Because of the assumptions the Boltzmann equation can be linearized about a streaming Maxwellian provided that alpha VM LS TH 1 and alpha M VM LS TH 1, where alpha and M are the accommodation coefficient at the plate surface and the Mach number respectively. The collisions in the linearized kinetic equation are described by the BGK model. The resulting equation is Fourier transformed, and a linear system involving the unknown Fourier transformed density, velocity and temperature perturbations is obtained. It is shown that the calculation of the coefficients of the system can be reduced to the evaluation of only two one-dimensional integrals, one of which is essentially the plasma dispersion function. This circumstance is particularly relevant for the numerical computation of the Fourier transforms and its inversion.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/657375
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