Beyond Flux-limited Diffusion: Parallel Algorithms for Multidimensional Radiation Hydrodynamics

This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here encapsulate the physics provided by the serial algorithm of Stone et al. but add new functionality both with regard to physics and numerics. In detailing our method, we have documented both the analytic and discrete forms of the radiation moment solution and the variable tensor Eddington factor (VTEF) closure term. We have described three different methods for computing a short-characteristic formal solution to the transfer equation, from which our VTEF closure term is derived. Two of these techniques include time dependence, a primary physics enhancement of the method not present in the Stone algorithm. An additional physics modification is the adoption of a matter-radiation coupling scheme which is particularly robust for nonequilibrium problems and which also reduces the operations cost of our radiation moment solution. Two key numerical components of our implementation are highlighted: the biconjugate gradient linear system solver, written for general use on massively parallel computers, and our techniques for parallelizing both the radiation moment solution and the transfer solution. Additionally, we present a suite of test problems with a much broader scope than that covered in the Stone work; new tests include nonequilibrium Marshak waves, two-dimensional ``shadow'' tests showing the one-sided illumination of an opaque cloud, and full RHD+VTEF calculations of radiating shocks. We use the results of these tests to assess the virtues and vices of the method as currently implemented, and we identify a key area in which the method may be improved. We conclude that radiation moment solutions closed with variable tensor Eddington factors show a qualitative improvement over results obtained with flux-limited diffusion, and further that this approach has a bright future in the context of parallel RHD simulations in astrophysics.