Application of the Finite-Element-with-Discontinuous-Support Method to Thermal Radiation Transport

Previous work has developed the Finite-Element-with-Discontiguous Support (FEDS) method for discretizing the energy variable for neutron transport (NT) using discontiguous and discontinuous finite elements in energy. Like nuclear cross sections for NT, atomic opacities in thermal radiation transport (TRT) exhibit rapid oscillations as a function of particle energy. These oscillations are difficult to treat numerically with the popular multigroup (MG) discretization when the number of degrees of freedom (DOF) in energy (the number of groups) is much less than the number of lines, which is often the case. These interaction similarities motivate us to apply the FEDS method to TRT problems. We derive FEDS for TRT and compare with MG as a function of number of DOF in energy for a wall-heating problem, finding FEDS often is more consistently convergent and has lower error than MG for the same number of DOF.