Multigroup linear transport in the exponential half-space—II

Abstract

The multigroup half-space exit distribution problem in an exponential atmosphere is considered by two separate approaches. The first approach consists of an expansion of the multigroup angular flux solution in a half-range complete set of eigenfunctions. Then, through an orthogonality relation between these eigenfunctions and those of the adjoint transport equation, a set of singular integral equations is derived for the multigroup exit distributions. The half-range completeness of the eigenfunctions is then shown to imply that these singular integral equations possess a unique solution. The second approach consists of deriving this same set of singular integral equations by Laplace transforming the set of integral equations for the scalar group fluxes. Uniqueness of the solution is also shown in an appropriate function space. A multigroup version of the F-N method is then formulated and applied to the solution of the set of singular integral equations. Convergence is proven and the numerical results for the two group albedo is seen to be in good agreement with those obtained from the standard S-N method calculations.