A Diffusion-Accelerated Solution Method for the Nonlinear Characteristic Scheme in Slab Geometry

Recently, the nonlinear characteristic (NC) scheme for spatially discretizing the discrete ordinates equations was introduced. This scheme is accurate for both optically thin and optically thick spatial meshes and produces strictly positive angular fluxes. The NC discrete ordinates equations can be solved using the source iteration method; however, it is well known that this method converges prohibitively slowly for optically thick problems with scattering ratios at or near unity. A general nonlinear diffusion synthetic acceleration method for solving the NC equations in slab geometry is described. Numerical results to show the effectiveness and efficiency of the new solution method are provided.