Asymptotic Behavior of the Solution of the Integral Transport Equation in Slab Geometry

1977 ◽  
Vol 32 (1) ◽  
pp. 191-200 ◽  
Author(s):  
Hans G. Kaper ◽  
R. Bruce Kellogg
Keyword(s):  
Asymptotic Behavior ◽  
Transport Equation ◽  
Slab Geometry ◽  
Integral Transport

Solution of the Transport Equation with Anisotropic Scattering in Slab Geometry

1968 ◽  
Vol 9 (5) ◽  
pp. 753-759 ◽  
Author(s):  
Robert L. Bowden ◽  
F. Joseph McCrosson ◽  
Edgar A. Rhodes
Keyword(s):  
Transport Equation ◽  
Anisotropic Scattering ◽  
Slab Geometry

Approximate solutions to the half-space integral transport equation near a plane boundary

1980 ◽  
Vol 58 (9) ◽  
pp. 1291-1310 ◽  
Author(s):  
Michael S. Milgram
Keyword(s):  
Transport Equation ◽  
Half Space ◽  
Matrix Multiplication ◽  
Solution Space ◽  
Plane Geometry ◽  
Plane Boundary ◽  
Infinite Plane ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Integral Transport

A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.

Sign in / Sign up

Export Citation Format

Share Document