HIGH-ORDER BACKWARD DISCRETIZATION OF THE NEUTRON DIFFUSION EQUATION

Fast codes capable of dealing with three-dimensional geometries, are n eeded to be able to simulate spatially complicated transients in a nuc lear reactor. We propose a new discretization technique for the time i ntegration of the neutron diffusion equation, based on the backward di fference formulas for systems of stiff ordinary differential equations . This method needs to solve a system of linear equations for each int egration step, and for this purpose, we have developed an iterative bl ock algorithm combined with a variational acceleration technique. We t ested the algorithm with two benchmark problems, and compared the resu lts with those provided by other codes, concluding that the performanc e and overall agreement are very good. (C) 1997 Elsevier Science Ltd.