Advanced computational methods for nodal diffusion, Monte Carlo, and S{sub N} problems. Progress report, January 1, 1992--March 31, 1993 [report]

W.R. Martin
1993 unpublished
This proposal describes progress on five separate research efforts for improv; ng the effectiveness of computational methods for particle diffusion and transport problems. These are: • The development of multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme has been found to be promising and is being implemented into a nodal diffusion code. In addition, simplified P2 has been implemented into this code with excellent
more » ... ith excellent results compared to transport calculations. • The development of the Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work has been very successful, yielding predictions for both 1-D and 2-D x-y geometry which are significantly better than conventional Monte Carlo with splitting and Russian Roulette. • The implementation of Asymptotic Diffusion Synthetic Acceleration methods for ebtaining accurate and rapidly converging solutions of certain 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. • The development of Quasidiffusion (QD) methods for obtaining accurate and rapidly converging solutions of multidimensional SN problems on irregular spatial grids. A "symmetrized" QD method has been developed and implemented in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. • The implementation of the response history method for speeding up the Monte Carlo calculation of electron transport problems. Although this effort was not funded during the first year of the project, we have been able to implement the response history method 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. Progress on these projects has greatly enhanced our ability to obtain accurate and efficient I solutions for many diffusion and transport problems encountered in nuclear engineering ,' applications t < 2 zI
doi:10.2172/10115397 fatcat:nejau5pkjfgdjp47rt3k3p2j7y