Advanced computational methods for nodal diffusion, Monte Carlo, and S[sub N] problems

Abstract

This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.