Relativistic magnetohydrodynamics in dynamical spacetimes: A new adaptive mesh refinement implementation

Journal Article · Fri Oct 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.084031· OSTI ID:21433013

Etienne, Zachariah B; Liu, Yuk Tung ^[1]; Shapiro, Stuart L

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1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)

We have written and tested a new general relativistic magnetohydrodynamics code, capable of evolving magnetohydrodynamics (MHD) fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the Baumgarte-Shapiro Shibata-Nakamura formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential, which exists on a grid that is staggered with respect to the hydrodynamic and metric variables. The divergenceless constraint {nabla}{center_dot}B=0 is enforced by the curl of the vector potential. Our MHD scheme is fully compatible with AMR, so that fluids at AMR refinement boundaries maintain {nabla}{center_dot}B=0. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We present code validation test results, both in Minkowski and curved spacetimes. They include magnetized shocks, nonlinear Alfven waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.

• OSTI ID: 21433013
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALFVEN WAVES
BLACK HOLES
CONVERGENCE
EINSTEIN-MAXWELL EQUATIONS
ENERGY RANGE
EQUATIONS
EXPLOSIONS
FIELD EQUATIONS
FIELD THEORIES
FLUID MECHANICS
FLUIDS
FOUR-DIMENSIONAL CALCULATIONS
GENERAL RELATIVITY THEORY
HYDRODYNAMICS
HYDROMAGNETIC WAVES
MAGNETOHYDRODYNAMICS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MECHANICS
METRICS
MINKOWSKI SPACE
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
RELATIVISTIC RANGE
RELATIVITY THEORY
RESOLUTION
SIMULATION
SPACE
SPACE-TIME