Doctoral Dissertations

Abstract

"In this work we investigate the applicability of a "Boundary Element method 11 for the numerical solution of the Liouville and Helmholtz eigenvalue problem for different two-dimensional geometries including a typical reactor configuration. The method is based on the discretization of the unknown along the boundary and Green's function representation of the governing equation.

To compare the capability of this method with the finite element method, a finite element code which uses quadratic quadrilateral isoperimetric elements was developed. A boundary element code was also written. These codes were used to determine the fundamental eigenvalue for several two-dimensional geometries -- square, "L" shaped, circular, and a quarter of a typical reactor core. The results of both codes were compared with each other and with analytical solutions where available. To optimize the computer time for the code based on the boundary element method, a powerful search technique called Fibonacci search was used to determine the fundamental eigenvalues.

During the course of this study, it was found that eliminating the imaginary part of the fundamental solution of the Helmholtz equation produced an instability in the result. The results show that, due to the use of the iteration procedure in the boundary element method to evaluate the determinant of the deduced matrix, more computer time is required for the boundary element solution than the finite element solution. However, the results obtained on the basis of the boundary element technique are more accurate than those from the finite element method"-- Abstract pp. iii-iv

Advisor(s)

Edwards, D. R.

Committee Member(s)

Tsoulfanidis, Nicholas
Dolan, Tom
Gillett, Billy E.
Keith, Harold D. (Harold Dean), 1941-

Department(s)

Nuclear Engineering and Radiation Science

Degree Name

Ph. D. in Nuclear Engineering

Publisher

University of Missouri--Rolla

Publication Date

Spring 1982

Pagination

xi, 160 pages

Note about bibliography

Includes bibliographical references (pages 53-60).

Rights

© 1982 Farough Baradari, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Nuclear reactors Eigenvalues Boundary element methods Finite element method

Thesis Number

T 4667

Print OCLC #

9268184

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