Degree Type

Dissertation

Date of Award

1989

Degree Name

Doctor of Philosophy

Department

Nuclear Engineering

First Advisor

A. F. Rohach

Abstract

A modular nodal method is developed for solving the neutron transport equation by using the spherical harmonics approximation in two dimensional Cartesian coordinates. The spherical harmonics approximation is based upon the second order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation are manipulated to have the forms analogous to the partial currents in the neutron diffusion equation. The relationships are developed for generating both the second order spherical harmonic equations and the boundary conditions in an automatic manner. The nodal method developed is based upon a least squares minimization technique. In that method, the spherical harmonic moments are expanded into fourth order Legendre polynomials. While some of the unknown coefficients are determined through the equations provided by the minimization scheme, the others are obtained through implementation of the boundary conditions in an integral sense. The order of the P[subscript]n approximation in the nodes are determined by the developed scheme in automatic manner. The distribution of the approximations orders may be different in different parts of the problem domain.

DOI

https://doi.org/10.31274/rtd-180813-12630

Publisher

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

Copyright Owner

Feyzi Inanc

Language

en

Proquest ID

AAI8920145

File Format

application/pdf

File Size

127 pages

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