Finite element projection method for the solution of particle transport problems with anisotropic scattering

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1983

OSTI ID:5869736

Wills, E E

A solution method for solving particle transport problems was 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 solution method is developed as a complementary alternative to the standard solution techniques of discrete ordinates, Monte Carlo, and the P/sub r/ method.

• Research Organization: New Mexico Univ., Albuquerque (USA)
• OSTI ID: 5869736
• Country of Publication: United States
• Language: English

Related Subjects

654001* -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANISOTROPY
FINITE ELEMENT METHOD
MANY-DIMENSIONAL CALCULATIONS
MULTIGROUP THEORY
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
PARTICLE KINEMATICS
RITZ METHOD
SPHERICAL HARMONICS
TRANSPORT THEORY
VARIATIONAL METHODS