Reduced Memory Space-Time Discretization Schemes for High-Energy-Density Physics

This talk presents implicit space-time discretization methods with reduced memory for approximation of the radiative transfer equation (RTE) and their application in thermal radiative transfer and radiation hydrodynamics simulations. The reduced-memory methods (RMMs) are formulated for the RTE discretized with the backward-Euler time integration scheme and the bilinear-discontinuous (BLD) finite element method in space. The BLD scheme requires a spatial degree of freedom at each corner of a cell. The RMMs store only the cell-average value of the specific intensity within each cell between timesteps, reducing the persistent memory allocation requirement to just one value per cell. At the new time step, the RMMs utilize spatial reconstruction schemes to approximate the numerical solution at each spatial degree of freedom of the BLD scheme. We developed the RMMs with different spatial reconstruction techniques: zero-slope approximation, linear and bilinear interpolation functions. We analyzed convergence in space and time of the developed RMMs using a set of tests with manufactured solutions. Numerical results for thermal radiative transfer and radiation hydrodynamics problems in 2D Cartesian and axisymmetric (r-z) geometries will be presented to demonstrate performance of the proposed RMMs.