Nonlinear methods for solving the diffusion equation
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857233436.pdf
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8.05 MB
Format
Adobe PDF
Checksum (MD5)
4932918e25f179586eb0640f8f7d9074
Author(s)
Shober, Robert Anthony
Henry, Allan F.
Date Issued
1976
Publisher
Cambridge, Mass. : Massachusetts Institute of Technology, Dept. of Nuclear Engineering, [1976]
Series/Report no.
MITNE ; no. 196
Report (Electric Power Research Institute)
Abstract
This thesis is concerned with methods for the transient solution of the neutron diffusion equations in one or two energy groups. Initially, nonlinear methods for solving the static diffusion equations using the finite element method were investigated. By formulating a new eigenvalue equation, some improvement in the solution efficiency was obtained. However, the transient solution of the diffusion equation using the finite element method was considered to be overly expensive. An analytic method for solving the one-dimensional diffusion equation was then developed. Numerical examples confirmed that this method is exact in one dimension. The method was extended to two dimensions, and results compared employing two different approximations for the transverse leakage. The method based on a flat approximation to the leakage was found to be superior, and it was extended to time-dependent problems. Results of time-dependent test problems show the procedure to be accurate and efficient. Comparisons with conventional finite difference techniques (such as TWIGL or MEKIN) indicate that the scheme can be an order of magnitude more cost effective.
Description
"November, 1976."
Also issued as a Ph. D. thesis written by the first author and supervised by the second author, MIT Dept. of Nuclear Engineering, 1977
Includes bibliographical references (pages 112-116)
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