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

Abstract

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 (1992), 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 dramatic 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.Subject headings: hydrodynamics -methods:numerical -methods:parallel -radiative transfer the radiation field within a medium in which both light-crossing timescales and (far longer) thermal timescales are important. The test problem specified for benchmarking a new algorithm was the "tophat" (or "crooked pipe") test, a description of which is given by Gentile (2001). The algorithm desired was one that could capture the aforementioned features of the problem at a fraction of the cost of more elaborate Boltzmann (e.g. S n ) or Monte Carlo methods. We felt that a moment-based approach like that described in Paper III was an ideal candidate for treating the tophat test, and further that the original serial method could be adapted for parallel use.The final product of this project is a new set of numerical routines for performing RHD simulations in a parallel environment. These routines provide all of the abilities advertised for the serial rou...

Radiation hydrodynamics with adaptive mesh refinement and application to prestellar core collapse

“…The spike's amplitude varies according to the model used for radiation and to the effective numerical resolution. Thanks to the AMR scheme, the spike's amplitude is larger in the supercritical case, but not as large as those obtained with M1 or VTEF models (Hayes & Norman 2003;González et al 2007). However, this last test shows the ability of our time-splitting method to integrate the RHD equations.…”

“…Mihalas & Mihalas 1984;Lowrie et al 2001;Mihalas & Auer 2001;Krumholz et al 2007b). Radiation hydrodynamics (RHD) methods have been developed in grid-based codes (Stone & Norman 1992;Hayes & Norman 2003;Krumholz et al 2007a;Kuiper et al 2010;Sekora & Stone 2010;Tomida et al 2010) and also in smoothed particles hydrodynamics (SPH) codes (Boss et al 2000;Whitehouse & Bate 2006;Stamatellos et al 2007). Most of these studies use the popular flux-limited diffusion approximation (FLD, e.g.…”

Star Formation with Adaptive Mesh Refinement Radiation Hydrodynamics

“…Higher order moment methods exist and can solve some of these problems (e.g. variable tensor Eddington factor methods, Hayes & Norman 2003, and the M1 closure method, González et al 2007), but none have yet proven cheap and robust enough for use in practical AMR star formation simulations. Frequency resolution.…”

Cosmological Radiation Hydrodynamics with Enzo

“…These describe conservation of mass (1), conservation of momentum (2), conservation of energy (3), chemical rate equations (4), flux-limited diffusion radiative transfer (5) and Poisson's equation (6), in a coordinate system that is comoving with the expanding universe [8,9,10,1]. The independent variables in these equations consist of the comoving baryonic density ρ b , the proper peculiar baryonic velocity v b , the total gas energy per unit mass e, the comoving number density for each chemical species n i , i = 1, .…”

“…Here κ T = κ + κ S is the total extinction coefficient, where κ is the opacity and κ S results from scattering [18]. The function (12) has been reformulated from its original version [9] to provide increased stability for scatteringfree simulations involving extremely small opacities (i.e. κ T = κ ≪ 1), as is typical in cosmology applications.…”