Constrained transport and adaptive mesh refinement in the Black Hole Accretion Code

Abstract

Context. Worldwide very-long-baseline radio interferometry (VLBI) arrays are expected to obtain horizon-scale images of supermassive black hole candidates as well as of relativistic jets in several nearby active galactic nuclei. This, together with the expected detection of electromagnetic counterparts of gravitational-wave signals, motivates the development of models for magnetohydrodynamic flows in strong gravitational fields. Aims. The Black Hole Accretion Code (BHAC) is a publicliy available code intended to aid with the modelling of such sources by performing general relativistic magnetohydrodynamical (GRMHD) simulations in arbitrary stationary spacetimes. New additions to the code are required in order to guarantee an accurate evolution of the magnetic field when small and large scales are captured simultaneously. Methods. We discuss the adaptive mesh refinement (AMR) techniques employed in BHAC, essential to keep several problems computationally tractable, as well as staggered-mesh-based constrained transport (CT) algorithms to preserve the divergence-free constraint of the magnetic field, including a general class of prolongation operators for face-allocated variables compatible with them. Results. After presenting several standard tests for the new implementation, we show that the choice of divergence-control method employed can produce qualitative differences in the simulation results for scientifically relevant accretion problems. We demonstrate the ability of AMR to decrease the computational costs of black-hole accretion simulations while sufficiently resolving turbulence arising from the magnetorotational instability. In particular, we describe a simulation of an accreting Kerr black hole in Cartesian coordinates using AMR to follow the propagation of a relativistic jet while self-consistently including the jet engine, a problem set up-for which the new AMR implementation is particularly advantageous. Conclusions. The CT methods and AMR strategies discussed here are being currently employed in the simulations performed with BHAC used in the generation of theoretical models for the Event Horizon Telescope Collaboration.

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project

“…The algorithm is centered on second-order finite-volume methods, and various schemes for the treatment of the magnetic field update have been implemented on ordinary and staggered grids. More details on the various •  B preserving schemes and their implementation in BHAC can be found in Olivares et al (2018Olivares et al ( , 2019. Originally designed to study BH accretion in ideal MHD, BHAC has been extended to incorporate nuclear equations of state, neutrino leakage, charged and purely geodetic test particles (Bacchini et al 2018(Bacchini et al , 2019, and nonblack-hole fully numerical metrics.…”

MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit

“…The BHAC code has recently been extended with an IMEX scheme to handle the extension to general relativistic, resistive MHD equations [69], where all covariant Maxwell equations, especially also those for electric field evolutions, enter. The IMEX scheme then treats the stiff resistive source terms, and can use a staggered representation of the GR(R)MHD variables, to ensure that magnetic monopoles only occur at machine precision [70]. The code structure and modularity, especially in its parallelization and AMR strategy, is fully shared between the MPI-AMRVAC and BHAC code efforts.…”

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

“…We presented the implementation of a resistive module in the general-relativistic magneto-fluid code BHAC. The new GRRMHD algorithm is tested and used in this work in combination with AMR and a recently implemented staggered CT method to ensure solenoidal magnetic fields (Olivares et al 2018(Olivares et al , 2019.…”

“…Our implementation of the GRRMHD equations enforces Equation (29) to roundoff error by means of the staggered CT scheme of Balsara & Spicer (1999), whose implementation in BHAC has been presented in detail by Olivares et al (2019). The charge density is obtained by numerically taking the divergence of the evolved electric field as in Equation (32).…”

“…Adopting criteria that are based on the properties of the plasma dynamics, a finer grid is introduced in order to accurately resolve smaller scales in a confined area, thus dramatically reducing the computational costs (Keppens et al 2003;Porth et al 2017). A constrained transport (CT) method that is compatible with AMR is employed to keep the divergence of the magnetic field equal to machine precision at all times (Olivares et al 2018(Olivares et al , 2019. The algorithm is developed to solve the GRRMHD equations in any spacetime metric in one, two, or three spatial dimensions.…”