Nested Element Method in Multidimensional Neutron Diffusion Calculations

Abstract

A new numerical method is developed that is particularly efficient in solving the multidimensional neutron diffusion equation in geometrically complex systems. The needs for a generally applicable and fast running computer code have stimulated, here presented, the inroad of a nonclassical (R-function) numerical method into the nuclear field. By using the R-functions, the geometrical components of the diffusion problem are a priory analytically implemented into the approximate solution. The class of functions, to which the approximate solution belongs, is chosen as close to the exact solution class as practically acceptable from the time const.mpticn point of view. That implies a drastic reduction of the number of degrees of freedom, compared to the other methods. Furthermore, the reduced number of degrees of freedom enables calculation of large multidimensional problems on small computers.