Solution to the linear BGK equation via the principles of invariance

B. D. Ganapol

doi:10.1088/0305-4470/29/6/010

Solution to the linear BGK equation via the principles of invariance

B. D. Ganapol

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Abstract

The solution to the linearized BGK equation of kinetic theory is obtained via the principles of invariance as formulated by Chandrasekhar. The solution represents an alternative to the singular eigenfunction method featuring regular integral equations which are more easily evaluated. Laplace transforms are obtained for the net flow velocity and velocity distribution for both the albedo and Milne problems with wall reflection. The transforms are then numerically inverted to a high degree of accuracy. Results are compared to those of Kainz and Titulaer.

Original language	English (US)
Pages (from-to)	1227-1244
Number of pages	18
Journal	Journal of Physics A: Mathematical and General
Volume	29
Issue number	6
DOIs	https://doi.org/10.1088/0305-4470/29/6/010
State	Published - 1996

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/29/6/010

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abstract = "The solution to the linearized BGK equation of kinetic theory is obtained via the principles of invariance as formulated by Chandrasekhar. The solution represents an alternative to the singular eigenfunction method featuring regular integral equations which are more easily evaluated. Laplace transforms are obtained for the net flow velocity and velocity distribution for both the albedo and Milne problems with wall reflection. The transforms are then numerically inverted to a high degree of accuracy. Results are compared to those of Kainz and Titulaer.",

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AB - The solution to the linearized BGK equation of kinetic theory is obtained via the principles of invariance as formulated by Chandrasekhar. The solution represents an alternative to the singular eigenfunction method featuring regular integral equations which are more easily evaluated. Laplace transforms are obtained for the net flow velocity and velocity distribution for both the albedo and Milne problems with wall reflection. The transforms are then numerically inverted to a high degree of accuracy. Results are compared to those of Kainz and Titulaer.

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Solution to the linear BGK equation via the principles of invariance

Abstract

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