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

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  • An Analysis of Discretization for Solutions of the Diffusion Equation Using Mesh Centered Finite Differences(1)XYZ Geometry
  • Analysis of Discretization for Solution

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Abstract

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.

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