A Two-Grid and Nonlinear Diffusion Acceleration Method for the SN Equations with Neutron Upscattering

Abstract

Nonlinear diffusion acceleration (NDA), also known as coarse-mesh finite difference, is a well-known technique that can be applied to accelerate the scattering convergence in neutronics calculations. In multigroup problems, NDA is effective in conjunction with a Gauss-Seidel iteration in energy when there is not much upscattering. However, in the presence of significant upscattering, which occurs in many materials commonly used in nuclear applications, the efficiency of Gauss-Seidel with NDA degrades. A two-grid (TG) acceleration scheme was developed by Adams and Morel for use with standard, unaccelerated SN problems and Gauss-Seidel. Inspired by this two-grid scheme, we derive a new two-grid scheme specific to the NDA equation, which we are calling TG-NDA. By applying the method to several test problems, we find TG-NDA to be a successful acceleration method for problems with significant upscattering.