The suite of analytical benchmarks for neutral particle transport in infinite isotropically scattering media

Journal Article · Wed Jan 01 04:00:00 EST 1997 · Nuclear Science and Engineering

OSTI ID:445401

Kornreich, D E ^[1]; Ganapol, B D ^[2]

---

1. Los Alamos National Lab., NM (United States)
2. Univ. of Arizona, Tucson, AZ (United States). Dept. of Nuclear Engineering

The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality evaluations of solutions for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is isotropic. The solutions are generally obtained through the use of Fourier transform methods with the numerical inversions constructed from standard numerical techniques such as Gauss-Legendre quadrature, summation of infinite series, and convergence acceleration. Consideration of the suite of benchmarks in infinite homogeneous media begins with the standard one-dimensional problems: an isotropic point source, an isotropic planar source, and an isotropic infinite line source. The physical and mathematical relationships between these source configurations are investigated. The progression of complexity then leads to multidimensional problems with source configurations that also emit particles isotropically: the finite line source, the disk source, and the rectangular source. The scalar flux from the finite isotropic line and disk sources will have a two-dimensional spatial variation, whereas a finite rectangular source will have a three-dimensional variation in the scalar flux. Next, sources emitting particles anisotropically are considered. The most basic such source is the point beam giving rise to the Green`s function, which is physically the most fundamental transport problem, yet may be constructed from the isotropic point source solution. Finally, the anisotropic plane and anisotropically emitting infinite line sources are considered. Thus, a firm theoretical and numerical base is established for the most fundamental neutral particle benchmarks in infinite homogeneous media.

• OSTI ID: 445401
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 125; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BENCHMARKS
BOLTZMANN EQUATION
ISOTROPY
NEUTRAL-PARTICLE TRANSPORT
NUMERICAL SOLUTION
RADIATION FLUX
RADIATION SOURCES