Diffusion-Accelerated Solution of the Two-Dimensional X-Y S_n Equations with Linear-Bilinear Nodal Differencing

Recently, a new diffusion synthetic acceleration scheme was developed for solving the two-dimensional S_n equations in x-y geometry with bilinear-discontinuous finite element spatial discretization, by using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differed from previous methods in that it is unconditionally efficient for problems with isotropic or nearly isotropic scattering. Here, the same bilinear-discontinuous diffusion differencing scheme, and associated multilevel solution technique, is used to accelerate the x-y geometry S_n equations with linear-bilinear nodal spatial differencing. It is found that for problems with isotropic or nearly isotropic scattering, this leads to an unconditionally efficient solution method. Computational results are given that demonstrate this property.