Thermal radiative transfer (TRT) is a dominant mechanism of energy transfer in the high energy density regimes found in astrophysical phenomena and inertial confinement fusion experiments.
Kinetic models of TRT offer the physics fidelity needed to reduce the gap between simulation and experiment observed in high energy density physics (HEDP) but with orders of magnitude more computational cost than less accurate, continuum models of the radiation field. Moment methods are a class of scale and modeling-bridging algorithms centered around the use of reduced-dimensional models, known as the moment equations, to accelerate the iterative solution of radiation transport. These methods have the potential to significantly reduce the cost of simulating radiation transport in the HEDP multiphysics context but have not been used in large-scale simulations due to the lack of scalable solvers for the unusual mathematical structure of the moment equations. In this talk, the flexibility of the moment algorithm is leveraged to design discretizations for the moment equations that can be scalably solved with existing preconditioned iterative solver technology. This is achieved by extending the Discontinuous Galerkin, mixed finite element, and continuous finite element techniques developed for standard elliptic problems, along with their associated efficient preconditioned iterative solvers, to the unusual structure of the moment systems. The efficacy of the resulting radiation transport algorithms are demonstrated on challenging proxy problems from TRT and are shown to scale in parallel.
