Recent advances in spectral nodal methods for X,Y-geometry discrete ordinates deep penetration and eigenvalue problems

We describe the recent advances in a class of nodal methods applied to mult idimensional discrete ordinates (SN) transport problems in Cartesian geomet ry. This class of coarse-mesh methods is referred to as spectral nodal meth ods. The basic numerical schemes that we present are the spectral Green's f unction (SGF) nodal method and the spectral diamond (SD) nodal method. Firs t we describe a spectral nodal method applied to monoenergetic X,Y-geometry deep penetration S-N problems with flat approximations for the transverse leakage terms of the transverse integrated SN nodal equations. This method is referred to as the SGF constant nodal (SGF-CN) method. Furthermore, we d escribe the SGF exponential nodal (SGF-ExpN) method, wherein the transverse leakage terms are approximated by exponential functions. Next, we describe a hybrid spectral nodal method applied to monoenergetic X,Y-geometry SN ei genvalue problems with flat approximations for the transverse leakage terms of the transverse integrated SN nodal equations. For the multiplying regio ns of the nuclear reactor core, e.g. the fuel regions, we use the SD consta nt nodal (SD-CN) method, and for the non-multiplying regions, e.g. the refl ector regions, we use the SGF-CN method. Numerical results are given to ill ustrate the accuracy of each method presented. (C) 1999 Published by Elsevi er Science Ltd. All rights reserved.