CONSERVATIVE NONLINEAR DIFFUSION ACCELERATION APPLIED TO THE UNWEIGHTED LEAST-SQUARES TRANSPORT EQUATION IN MOOSE

摘要

Many second-order forms of the transport equation are not usable in voids and experience numerical convergence difficulties in near-voids. Here we consider a recently introduced least-squares form of the transport equation that is compatible with voids. Our purpose is to describe a nonlinear diffusion acceleration scheme that we have developed for a multidimensional multigroup form of this equation, that was implemented in Idaho National Laboratory's finite-element code, MOOSE. A deficiency of the least-squares equation is that it is not conservative. We compensate for this lack of conservation by coupling it with a conservative low-order drift-diffusion equation. Upon iterative convergence, the two equations do not necessarily yield the same solutions for the scalar flux and current except in the limit as the spatial mesh is increasingly refined. The low-order solution is generally found to be more accurate than both the pure least-squares solution and the coupled high-order solution. Preliminary computational results are presented demonstrating the accuracy of the low-order solution and the iterative effectiveness of the acceleration method relative to a similar implementation for the SAAF transport equation.