WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics

Abstract

The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of γ -ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of generalrelativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code and assess its accuracy. Such tests range from the solution of relativistic Riemann problems in flat spacetime, over to the stationary accretion onto a Schwarzschild black hole and up to the evolution of oscillating magnetized stars in equilibrium and constructed as consistent solutions of the coupled Einstein-Maxwell equations.PACS numbers: 04.25. Dm, 95.30.Qd, 04.40.Dg, 97.60.Jd, 95.30.Sf

GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit

“…Since the scheme of [45] evolves the cell-averaged magnetic field values, it computes the change in the cell-centred fields as the average change in the face centred fields…”

“…The GRHydro module of the Einstein toolkit is a new, independently written code, and-in particular-the development is completely independent of the WhiskyMHD code [45], since the GRHydro development started from the GRHD (non-MHD) version of the Whisky code. Given its close interaction with the hydrodynamic evolution, the MHD routines are contained within the GRHydro package (or 'thorn', in the language of Cactus-based routines).…”

Three-dimensional evolution of differentially rotating magnetized neutron stars

“…For this purpose, several GRMHD codes constructed so far [25,27,28,45] have implemented either the constrained-transport (CT) [56] or flux-CT scheme [57]. In the code of implementing FMR or AMR algorithm, we are required to take an additionally special care when performing the prolongation and restriction procedures of magnetic fields in the refinement boundaries, as described in Refs.…”

“…This amplified magnetic field could have an impact on the dynamics of the mergers because it contributes to the angular momentum transport and the magnetic pressure may modify the structure of the objects formed after the merger. Motivated by this expectation, several groups have implemented the magnetohydrodynamics (MHD) code in the framework of numerical relativity [23][24][25][26][27][28]. These numerical codes developed have been applied to collapse of magnetized hypermassive neutron stars (HMNS) [29][30][31], magnetized neutron starblack hole binary merger [32,33], evolution of magnetized neutron stars [34][35][36], and magnetorotational collapse of massive stellar cores [24,37].…”

Linear wave propagation in relativistic magnetohydrodynamics

“…Expressions for the wave speeds, as obtained for different reference frames in relative motion to each other, have been used as basic ingredients for the current suite of relativistic magnetofluid codes. [4][5][6][7][8][9][10][11][12] Knowledge of the ͑fastest͒ characteristic speeds embedded in the relativistic MHD equations is essential to obtain time-step stability limits for explicit time-stepping strategies, while many modern RMHD codes use more complete information on all linear wave dynamics. This information is incorporated in the eigenvectors of the flux Jacobian, with the fluxes appearing in the governing hyperbolic equations for the conserved variables, typically formulated in a 3 + 1 formulation where a fixed laboratory frame is selected.…”