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Lie group invariant finite-difference schemes for the neutron diffusion equation

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Title: Lie group invariant finite-difference schemes for the neutron diffusion equation
Author(s): Jaegers, Peter James
Doctoral Committee Chair(s): Axford, Roy A.
Department / Program: Nuclear, Plasma, and Radiological Engineering
Discipline: Nuclear Engineering
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Mathematics Engineering, Nuclear
Abstract: Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.
Issue Date: 1994
Type: Text
Language: English
URI: http://hdl.handle.net/2142/21114
Rights Information: Copyright 1994 Jaegers, Peter James
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9503223
OCLC Identifier: (UMI)AAI9503223
 

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