A Numerical Method for General Relativistic Magnetohydrodynamics

Abstract

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, & Wilson and uses Evans & Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A onedimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfvén wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and nonrelativistic shock tubes. A series of one-and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-l tori that are subject to the magnetorotational instability.

Magnetohydrodynamics in full general relativity: Formulation and tests

“…After the saturation occurs, U mag /U disk0 relaxes to ∼ 0.02-0.2. These values indicate that the magnetic β parameter often referred in [21] is of order ∼ 10. These relaxed values are in good agreement with previous results obtained in the simulation with a fixed background [21].…”

“…VI B. Similar test in a fixed background spacetime of a black hole has been performed in [20,21]. Here, we perform the test in full general relativity replacing the black hole by a neutron star.…”

“…At the excision radius and outer boundaries, we impose the condition that the system is stationary. The (semi) analytic solution for the stationary Bondi flow is put as the initial condition, and we evolve for 100M following previous authors [20,21,10].…”

Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

“…When magnetic fields are present, the no-atmosphere approach is not suitable, and a very small positive density must be maintained outside the stars. Special techniques for dealing with the lowdensity region in MHD calculations have been explored in [29,30].…”

“…For this test, we evolve the same configuration used by [74], [29], and [30]. The sonic radius is at Schwarzschild (areal) radius r s = 8M , the accretion rate isṀ = 1, and the equation of state is Γ = 4/3.…”