An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows

A type of overlapping grid in spherical coordinates called the Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed several standard hydrodynamic tests producing results which are in very good agreement with analytic solutions. Moreover, the solutions obtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundary between the two grid patches. The code has also been successfully used to model astrophysically relevant situations, namely equilibrium polytropes, a Taylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to our results, the usage of the Yin-Yang grid greatly enhances the suitability and efficiency of 3D explicit Eulerian codes based on spherical polar coordinates for astrophysical flows.Comment: 15 pages, 17 figures, 2 tables, accepted for publication in A&

GiRaFFE: An Open-Source General Relativistic Force-Free Electrodynamics Code

We present GiRaFFE, the first open-source general relativistic force-free electrodynamics (GRFFE) code for dynamical, numerical-relativity generated spacetimes. GiRaFFE adopts the strategy pioneered by McKinney and modified by Paschalidis and Shapiro to convert a GR magnetohydrodynamic (GRMHD) code into a GRFFE code. In short, GiRaFFE exists as a modification of IllinoisGRMHD, a user-friendly, open-source, dynamical-spacetime GRMHD code. Both GiRaFFE and IllinoisGRMHD leverage the Einstein Toolkit's highly-scalable infrastructure to make possible large-scale simulations of magnetized plasmas in strong, dynamical spacetimes on adaptive-mesh refinement (AMR) grids. We demonstrate that GiRaFFE passes a large suite of both flat and curved-spacetime code tests passed by a number of other state-of-the-art GRFFE codes, and is thus ready for production-scale simulations of GRFFE phenomena of key interest to relativistic astrophysics.Comment: 23 pages, 4 figures. Consistent with published versio

A Two-Dimensional MagnetoHydrodynamics Scheme for General Unstructured Grids

We report a new finite-difference scheme for two-dimensional magnetohydrodynamics (MHD) simulations, with and without rotation, in unstructured grids with quadrilateral cells. The new scheme is implemented within the code VULCAN/2D, which already includes radiation-hydrodynamics in various approximations and can be used with arbitrarily moving meshes (ALE). The MHD scheme, which consists of cell-centered magnetic field variables, preserves the nodal finite difference representation of div(\bB) by construction, and therefore any initially divergence-free field remains divergence-free through the simulation. In this paper, we describe the new scheme in detail and present comparisons of VULCAN/2D results with those of the code ZEUS/2D for several one-dimensional and two-dimensional test problems. The code now enables two-dimensional simulations of the collapse and explosion of the rotating, magnetic cores of massive stars. Moreover, it can be used to simulate the very wide variety of astrophysical problems for which multi-D radiation-magnetohydrodynamics (RMHD) is relevant.Comment: 22 pages, including 11 figures; Accepted to the Astrophysical Journal. Higher resolution figures available at http://zenith.as.arizona.edu/~burrows/mhd-code

Fornax: a Flexible Code for Multiphysics Astrophysical Simulations

This paper describes the design and implementation of our new multi-group, multi-dimensional radiation hydrodynamics (RHD) code Fornax and provides a suite of code tests to validate its application in a wide range of physical regimes. Instead of focusing exclusively on tests of neutrino radiation hydrodynamics relevant to the core-collapse supernova problem for which Fornax is primarily intended, we present here classical and rigorous demonstrations of code performance relevant to a broad range of multi-dimensional hydrodynamic and multi-group radiation hydrodynamic problems. Our code solves the comoving-frame radiation moment equations using the M1 closure, utilizes conservative high-order reconstruction, employs semi-explicit matter and radiation transport via a high-order time stepping scheme, and is suitable for application to a wide range of astrophysical problems. To this end, we first describe the philosophy, algorithms, and methodologies of Fornax and then perform numerous stringent code tests, that collectively and vigorously exercise the code, demonstrate the excellent numerical fidelity with which it captures the many physical effects of radiation hydrodynamics, and show excellent strong scaling well above 100k MPI tasks.Comment: Accepted to the Astrophysical Journal Supplement Series; A few more textual and reference updates; As before, one additional code test include

Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation

The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. An unusual test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle

Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e. Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic magnetohydrodynamics equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic magnetohydrodynamics in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick accretion disks around a black hole prone to the magnetorotational instability.Comment: 18 pages, 8 figures, submitted to Ap