A finite element projection method for the solution of particle transport problems

Journal Article · Tue Jul 01 04:00:00 EDT 1986 · Nucl. Sci. Eng.; (United States)

OSTI ID:6992643

Wills, E; Roderick, N; McDaniel, P

A method for solving particle transport problems has been developed. In this method the particle flux is expressed as a linear and separable sum of odd and even components in the direction variables. Then a Bubnov-Galerkin projection technique and an equivalent variational Raleigh-Ritz solution are applied to the second-order transport equation. A dual finite element basis of polynomial splines in space and spherical harmonics in angle is used. The general theoretical and numerical problem formalism is carried out for a seven-dimensional problem with anisotropic scattering, time dependence, three spatial and two angular 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. Finally, the computational validation of the method is obtained by a computer solution to the monoenergetic steady-state air-over-ground problem in a cylindrical (r,z) geometry and with an exponentially varying atmosphere.

• Research Organization: McClellan Central Lab., McClellan Air Force Base, Sacramento, CA 95652
• OSTI ID: 6992643
• Journal Information: Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 93:3; ISSN NSENA
• 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
BOUNDARY CONDITIONS
CHARGED-PARTICLE TRANSPORT THEORY
COMPUTER CALCULATIONS
ENERGY DEPENDENCE
EQUATIONS
FINITE ELEMENT METHOD
FUNCTIONS
HARMONICS
INCIDENCE ANGLE
NUMERICAL SOLUTION
OSCILLATIONS
POLYNOMIALS
RITZ METHOD
SCATTERING
STEADY-STATE CONDITIONS
TIME DEPENDENCE
TRANSPORT THEORY