A Finite Element Projection Method for the Solution of Particle Transport Problems with Anisotropic Scattering.
Abstract
A solution method for solving particle transport problems has been developed. This solution approach embodies a finite element projection technique and a related equivalent variational Raleigh-Ritz formalism. Particle flux in the transport equation is expressed as a linear and separable sum of odd and even components in the direction variables. Then a classical variational principle is obtained and shown to be equivalent to a Bubnov-Galerkin projected solution. A dual finite element basis of polynomial splines in space and spherical harmonics in angle is used in the Bubnov-Galerkin equations. The general theoretical and numerical problem formalism is carried out in a 3-dimensional geometry with anisotropic scattering and with a piecewise constant energy dependence. This is a seven-dimensional problem with time dependence, three spatial and two angular or directional variables and with a multigroup treatment of the energy dependence. The boundary conditions for most physical problems of interest are dealt with explicitly and rigorously by a classical minimization (variational) principle. The computational validation of the method was obtained by a computer solution to the air-over-ground problem. This problem is of significant interest in the areas of nuclear weapons effects and radiation physics.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1984
- Accession Number
- ADA145382
Entities
People
- E. E. Wills
Organizations
- Air Force Institute of Technology