Analysis of Corner Balance Nonlinear Diffusion Acceleration and Moment-Based, Spatially Linear Transport Discretizations

The recently developed High-Order, Low-Order scheme for the solution of thermal radiative transfer problems is applied as an acceleration method to the neutral particle transport equation. The resulting Corner Balance Nonlinear Diffusion Acceleration (CB-NDA) is derived, and a stability analysis is performed in conjunction with moment-based, spatially linear discretizations. These spatial discretizations correspond to the lumped Linear Discontinuous (LD) and Linear Characteristic (LC) schemes, which possess the thick diffusion limit. The lumped LD and LC schemes satisfy corner balance equations, which in turn are used to derive the CB-NDA. Two variants of the CB-NDA include the net current and partial current formulations. Numerical results are presented that verify the theoretical predictions and implementation. Theoretical spectral radius from the analysis is verified by comparison to values from the numerical solution of a one-dimensional transport problem. Results indicate similar stability between the CB-NDA–accelerated lumped LD and LC schemes. The net current–based CB-NDA is found to be unstable whereas the partial current formulation remains stable over the range of scattering ratios and optical thicknesses.