Second-Order Accurate Method for Solving Radiation-Hydrodynamics

Second-order discretization for radiation-hydrodynamics is currently an area of great interest. Second-order methods used to solve the respective single-physics problems often differ fundamentally, making it difficult to combine them in a second- order manner. Here, we present a method for solving the equations of radiation hydrodynamics that is second-order accurate in space and time. We achieve this accuracy by combining modern methods used in standard single-physics calculations. This method is defined for a 1-D model of compressible fluid dynamics coupled with grey radiation diffusion and combines the MUSCL-Hancock method for solving the Euler equations with the TR/BDF2 scheme in time and a linear-discontinuous finite-element method in space for solving the equations of radiative transfer. Though uncommon for radiation diffusion calculations, the linear-discontinuous method is a standard for radiation transport applications. We address the challenges inherent to using different spatial discretizations for the hydrodynamics and radiation components and demonstrate how these may be overcome. Using the method of manufactured solutions, we show that the method is second-order accurate in space and time for both the equilibrium diffusion and streaming limit, and we show that the method is capable of computing radiative shock solutions accurately by comparing our results with semi-analytic solutions

A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations

Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of Computational Physic

A Hybrid Godunov Method for Radiation Hydrodynamics

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density and flux as well as a modified Godunov scheme for the material density, momentum density, and energy density. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati & Colella 2007. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61 pages, 15 figures, 11 table

Toward Five-dimensional Core-collapse Supernova Simulations

The computational difficulty of six-dimensional neutrino radiation hydrodynamics has spawned a variety of approximations, provoking a long history of uncertainty in the core-collapse supernova explosion mechanism. Under the auspices of the Terascale Supernova Initiative, we are honoring the physical complexity of supernovae by meeting the computational challenge head-on, undertaking the development of a new adaptive mesh refinement code for self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics. This code--called {\em GenASiS,} for {\em Gen}eral {\em A}strophysical {\em Si}mulation {\em S}ystem--is designed for modularity and extensibility of the physics. Presently in use or under development are capabilities for Newtonian self-gravity, Newtonian and special relativistic magnetohydrodynamics (with `realistic' equation of state), and special relativistic energy- and angle-dependent neutrino transport--including full treatment of the energy and angle dependence of scattering and pair interactions.Comment: 5 pages. Proceedings of SciDAC 2005, Scientific Discovery through Advanced Computing, San Francisco, CA, 26-30 June 200

A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate level-solve packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (PTC). We analyze the magnitude of the PTC parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the partial temperature scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. (Abridged)Comment: 46 pages, 14 figures, accepted to JC

A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics

We present the new code ALCAR developed to model multidimensional, multi energy-group neutrino transport in the context of supernovae and neutron-star mergers. The algorithm solves the evolution equations of the 0th- and 1st-order angular moments of the specific intensity, supplemented by an algebraic relation for the 2nd-moment tensor to close the system. The scheme takes into account frame-dependent effects of order O(v/c) as well as the most important types of neutrino interactions. The transport scheme is significantly more efficient than a multidimensional solver of the Boltzmann equation, while it is more accurate and consistent than the flux-limited diffusion method. The finite-volume discretization of the essentially hyperbolic system of moment equations employs methods well-known from hydrodynamics. For the time integration of the potentially stiff moment equations we employ a scheme in which only the local source terms are treated implicitly, while the advection terms are kept explicit, thereby allowing for an efficient computational parallelization of the algorithm. We investigate various problem setups in one and two dimensions to verify the implementation and to test the quality of the algebraic closure scheme. In our most detailed test, we compare a fully dynamic, one-dimensional core-collapse simulation with two published calculations performed with well-known Boltzmann-type neutrino-hydrodynamics codes and we find very satisfactory agreement.Comment: 30 pages, 12 figures. Revised version: several additional comments and explanations, results remain unchanged. Accepted for publication in MNRA

CASTRO: A New Compressible Astrophysical Solver. II. Gray Radiation Hydrodynamics

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.Comment: accepted for publication in ApJS, high-resolution version available at https://ccse.lbl.gov/Publications/wqzhang/castro2.pd

Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant'' initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.