First-Order Solutions of the One-Speed Transport Equation in Plane Multiregion Geometries
- 1 February 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (2) , 345-355
- https://doi.org/10.1063/1.1704939
Abstract
Case's method is applied to multiregion problems in plane geometry. Half‐range and ``two‐media'' orthogonality relations are used to obtain a system of coupled integral equations for the appropriate expansion coefficients. The system is explicitly solved in a first‐order approximation, which is valid for wide regions. Numerical analysis and comparison with transport computer codes indicates that such solutions are essentially exact for region thicknesses of five mean free paths or more.Keywords
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