An Analysis of Discretization for Solutions of the Diffusion Equation Using Mesh Centered Finite Differences (I)XYZ Geometry

In this paper eigenvalue mesh dependence is investigated for mesh centered finite difference approximations to the diffusion equation. The well known mesh squared variation of eigenvalue is quantified for XYZ geometry. The second part of the paper describes a method of significantly reducing mesh er...

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Bibliographic Details
Published in:Journal of nuclear science and technology 1998-11, Vol.35 (11), p.759-767
Main Author: FLETCHER, John Keith
Format: Article
Language:English
Subjects:
Applied sciences
eigenvalue
Energy
Energy. Thermal use of fuels
Exact sciences and technology
fast reactors
finite difference method
Fission nuclear power plants
Installations for energy generation and conversion: thermal and electrical energy
mesh effects
multigroup diffusion equation
reactor physics
Taylor's expansion
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Summary:In this paper eigenvalue mesh dependence is investigated for mesh centered finite difference approximations to the diffusion equation. The well known mesh squared variation of eigenvalue is quantified for XYZ geometry. The second part of the paper describes a method of significantly reducing mesh errors in diffusion theory finite difference codes. Essentially approximations to higher derivatives involving flux values at mesh points are used to generate a source which eliminates second order errors. The approach has been implemented in XYZ geometry and after a description of the technique results are presented for a series of test problems showing that almost zero mesh values can be obtained with the correction process.
ISSN:0022-3131
1881-1248
DOI:10.1080/18811248.1998.9733942