Analytical benchmark solutions via numerical transform inversion

Journal Article · Sat Dec 31 04:00:00 EST 1994 · Transactions of the American Nuclear Society

OSTI ID:89104

Ganapol, B D

In all elementary texts on transport theory of which this author is aware, the first problem demonstrated is for the Green`s function of the one-group transport equation in an infinite medium. Except for Case`s method, the solution is obtained via a Fourier transform. Even when demonstrating Case`s method, the point is usually made that Case`s method and the Fourier transform method are virtually identical. The inversion is then performed analytically, requiring the reader to recall how a residue is formed and how to integrate along branch cuts with no more reward at the end than having to deal with the evaluation of a relatively complicated integral if numerical results are desired. For those scientists, engineers, and applied mathematicians who do not wish to learn transport theory or complex variables but who are in need of the Green`s function solution, there is apparently little recourse - until now. With today`s {open_quotes}number crunching{close_quotes} computational environments and associated developments in numerical methods, numerical Fourier and Laplace transform inversions are relatively commonplace. For this reason with recently developed software contained in the {open_quotes}Analytical Benchmark Libran for Nuclear Engineering,{close_quotes} the scalar flux Green`s function solution even with anisotropic scattering can be obtained numerically with minimal input indicating only the desired relative error, the coefficients of the scattering kernel, and the spatial edit points. The same is true for transport in a half-space and will soon be true for transport in a slab. The solution method, its advantages and disadvantages, and a demonstration are presented.

• OSTI ID: 89104
• Report Number(s): CONF-941102--
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 71; ISSN 0003-018X; ISSN TANSAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ALBEDO
GREEN FUNCTION
INTEGRAL TRANSFORMATIONS
INTEGRALS
LAPLACE TRANSFORMATION
NEUTRON TRANSPORT THEORY