Five-point form of the nodal diffusion method and comparison with finite-difference

Conference · Fri Jan 01 04:00:00 EST 1988

OSTI ID:5154760

Azmy, Y Y

Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5154760
• Report Number(s): CONF-880601-3; ON: DE88004141
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990210 -- Supercomputers-- (1987-1989)
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FUNCTIONS
GREEN FUNCTION
ITERATIVE METHODS
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION