Towards High Order Accurate Thermal Radiative Transfer Solutions

Peter Maginot, Texas A&M University

Thermal radiative transfer calculations are important in several areas of physics and engineering: inertial confinement fusion, high energy density physics experiments, and the study of supernovae, to name a few. In slab geometry, the current state of the art is to use a full transport description of the angular intensity using linear discontinuous finite elements (LDFEM). In practice LDFEM is usually “lumped” – that is, the mass matrix is made to be diagonal – to improve the scheme’s “robustness” – resistance to negative angular intensities and oscillations. The benefit of using higher-order discontinuous finite element method (DFEM) trial spaces has been demonstrated in several areas outside of the nuclear engineering community. While higher-order DFEM have received some attention in the related field of neutron transport (nuclear reactors), significant work remains to demonstrate the viability and advantages of using higher order DFEM in thermal radiative transfer transport calculations.

In this poster we first demonstrate methods that can be used to create robust arbitrary order DFEM. Then we consider the effect of lumping on the order of accuracy/convergence of the method. Finally, we demonstrate the superior performance of arbitrary order DFEM compared to LDFEM for a prototypical thermal radiative transfer problem.

Abstract Author(s): Peter Maginot, Jean Ragusa, Jim Morel