Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Iterative solution of the diffusion and P1 finite element equations

Thesis/Dissertation ·
DOI:https://doi.org/10.2172/4067391· OSTI ID:4067391
 [1];  [2];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Univ. of Tennessee, Knoxville, TN (United States)
+ Show Author Affiliations
A method for obtaining solutions to the time-independent Boltzmann neutron transport equation on triangular grids with nonorthogonal boundaries and anisotropic scattering is developed. A functional is obtained from the canonical form of the multigroup transport equation. The angular variable is then removed by expanding the functional in spherical harmonics, retaining only the first two moments and limiting the anisotropic scattering to be linear. The finite element method is then implemented by using quadratic Lagrange-type interpolating polynomials to span the spatial domain. The resultant set of coupled linear equations is then solved iteratively. The applicability of convergence acceleration techniques developed for the finite difference method is tested and implemented where appropriate. Finally, a number of numerical experiments are performed to evaluate the performance of the proposed method. The results are compared to results obtained by various established methods. In all cases, agreement is excellent.
Research Organization:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
US Energy Research and Development Administration (ERDA)
DOE Contract Number:
W-7405-ENG-26
NSA Number:
NSA-33-027581
OSTI ID:
4067391
Report Number(s):
ORNL/TM--5224
Country of Publication:
United States
Language:
English

Similar Records

Solution of the finite element diffusion and P/sub 1/ equations by iteration
Journal Article · Wed Jun 01 00:00:00 EDT 1977 · Nucl. Sci. Eng.; (United States) · OSTI ID:7220293
Linear triangle finite element formulation for multigroup neutron transport analysis with anisotropic scattering
Technical Report · Sat May 01 00:00:00 EDT 1976 · OSTI ID:7184163
Advanced finite element techniques in reactor theory
Conference · Tue Dec 31 23:00:00 EST 1974 · OSTI ID:4112588

Related Subjects

*BOLTZMANN EQUATION-- NUMERICAL SOLUTION
*MULTIGROUP THEORY-- P1- APPROXIMATION
*NEUTRON DIFFUSION EQUATION-- NUMERICAL SOLUTION
22 GENERAL STUDIES OF NUCLEAR REACTORS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
FUNCTIONALS
INTERPOLATION
ITERATIVE METHODS
NEUTRON TRANSPORT THEORY
POLYNOMIALS
SERIES EXPANSION