A Two-Dimensional MagnetoHydrodynamics Scheme for General Unstructured Grids

Abstract

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.

22 pages, including 11 figures; Accepted to the Astrophysical Journal. Higher resolution figures available at http://zenith.as.arizona.edu/~burrows/mhd-code/

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• A New Multi-Dimensional General Relativistic Neutrino Hydrodynamics Code for Core-Collapse Supernovae II. Relativistic Explosion Models of Core-Collapse Supernovae
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• 2D Multi-Angle, Multi-Group Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores
• The Proto-neutron Star Phase of the Collapsar Model and the Route to Long-soft Gamma-ray Bursts and Hypernovae
• Magnetically-driven explosions of rapidly-rotating white dwarfs following Accretion-Induced Collapse
• The Role of Collective Neutrino Flavor Oscillations in Core-Collapse Supernova Shock Revival
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• Axisymmetric General Relativistic Simulations of the Accretion-Induced Collapse of White Dwarfs
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• Computational Models of Stellar Collapse and Core-Collapse Supernovae
• Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation