Collocation methods for space-time nuclear reactor dynamics

Thesis/Dissertation · Fri Jan 01 00:00:00 EST 1982

OSTI ID:6352390

Meade, D

The method of collocation of numerical analysis is applied in finding approximate solutions for the energy-group neutron diffusion and precursor concentration equations of space-time nuclear reactor dynamics. In the method of collocation, the unknown solution is approximated by a finite linear combination u hat of local basis functions containing adjustable constants or functions. These constants or functions are chosen by forcing the defect, Lu hat-f, zero at preselected points in the field. The so-called orthogonal collocation procedure used in the thesis basically involves determining an approximate solution by requiring it to satisfy the differential equation exactly at the affine images of the zeroes of the Legendre polynomials (Gaussian points). In contrast to the Galerkin approach, it does not require the evaluation of basis function products and numerical integration of scalar products. However, the stronger continuity conditions on the approximate solution demand a space of higher order element functions. After discretizing the space variables by collocation, the resulting system of ordinary differential equations is integrated by a version of the theta-methods. A collocation finite element group diffusion computer code COLFEM was developed to solve a one-dimensional two-energy group benchmark problem. Numerical results show excellent agreement with those obtained by the finite difference and Galerkin methods for several neutron diffusion and precursor time difference algorithms.

• Research Organization: California Univ., Berkeley (USA)
• OSTI ID: 6352390
• Resource Relation: Other Information: Thesis
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
REACTOR KINETICS
FINITE ELEMENT METHOD
SPACE DEPENDENCE
TIME DEPENDENCE
ALGORITHMS
BENCHMARKS
C CODES
COMPUTER CODES
GROUP THEORY
MESH GENERATION
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
KINETICS
MATHEMATICAL LOGIC
MATHEMATICS
220100* - Nuclear Reactor Technology- Theory & Calculation