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 se cond part of the paper describes a method of significantly reducing mesh er rors in diffusion theory finite difference codes. Essentially approximation s to higher derivatives involving flux values at mesh points are used to ge nerate a source which eliminates second order errors. The approach has been implemented in XYZ geometry and after a description of the technique resul ts are presented for a series of test problems showing that almost zero mes h values can he obtained with the correction process.