Accurate solutions to time dependent transport problems with a moving mesh and exact uncollided source treatments

Abstract

To find benchmark quality solutions to time dependent Sntransport problems, we develop a numerical method in a Discontinuous Galerkin (DG) framework that utilizes time dependent cell edges, called a moving mesh, and an uncollided source treatment. The moving mesh and uncollided source treatment is devised to circumvent discontinuities in the solution and better realize the potential of the DG method to converge on smooth problems. The resulting method achieves spectral convergence on smooth problems. When applied to problems with discontinuity-inducing sources, our combined method returns a significantly better solution than the standard DG method. On smooth problems, we observe spectral convergence even in problems with wave fronts. In problems where the angular flux is inherently non-smooth, we do not observe high-order of convergence when compared with static meshes, but there is a quantitative reduction in error of nearly three orders of magnitude.