Degree Type

Dissertation

Date of Award

1986

Degree Name

Doctor of Philosophy

Department

Nuclear Engineering

Abstract

Analyses have been made of the truncation error for the following finite difference approximations to the eigenvalue and boundary value problems evolving from the one-group neutron diffusion equation: (i) The seven-point relation; (ii) The fifteen-point relation; (iii) The nineteen-point relation; and (iv) The twenty-seven point relation. These methods have been derived using a Taylor series expansion technique and applied to the Laplacian operator contained in that equation in (x,y,z) geometry for various reactor configurations and boundary conditions;It has been shown that for methods ii and iii, a 4th order truncation error can be achieved, whereas for the 27-point approximation, a 6th order truncation error is possible;From the computer results of sample problems, considerable savings in accuracy (accurate eigenvalue and/or eigenfunctions) and system memory (fewer number of meshes required) can be obtained using the high order approximations, especially the 27-point relation, as compared to the 2nd order approximation.

DOI

https://doi.org/10.31274/rtd-180813-11993

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Mohammed Benghanem

Language

en

Proquest ID

AAI8703687

File Format

application/pdf

File Size

91 pages

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