Magnetohydrodynamics in full general relativity: Formulation and tests

The University of Tokyo, Tōkyō, Japan
Physical review D: Particles and fields (Impact Factor: 4.86). 07/2005; 72(4). DOI: 10.1103/PhysRevD.72.044014
Source: arXiv


A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a BSSN formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a longterm evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on. Comment: 28 pages, to be published in Phys. Rev. D

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    • "Consider for example the shallow water equations on the sphere [34] as a model for the global air and water flow and the " shallow water " magnetohydrodynamic equations [14] [27] as a model for the global dynamics in the solar tachocline. Further examples include surface acoustic waves [33], (magneto-)hydrodynamics in general relativity [11] [12] [28], the flow of oil on a moving water surface, the transport processes on cell surfaces [1] [26], surfactants on the interfacial hypersurface between two phases in multiphase flow [6], and the flow of a fluid in fractured porous media whose fractions are considered as a lower dimensional manifold [15]. Scalar conservation laws have been established as a good model problem for studying the nonlinear effects in such systems. "
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    ABSTRACT: In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L^\infty(M). In particular we show the existence and uniqueness of entropy solutions as well as the L^1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is allowed to depend on time and to have non-vanishing divergence. Furthermore, we derive estimates of the total variation of the solution for initial values in BV(M), and we give, in the case of a time-independent metric, a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates.
    Journal of Differential Equations 05/2012; 254(4). DOI:10.1016/j.jde.2012.11.002 · 1.68 Impact Factor
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    • "One such approach is known as the constraint transport technique [3] [4] which adopts a particular algorithm that staggers the variables appropriately to ensure the satisfaction of the constraint at round-off level within Finite Difference and Finite Elements techniques. This approach has been quite successful in a number of applications across different disciplines and particularly relevant in astrophysics applications [5] [6] [7] [8] [9] [10] [11] [12]. However, by design it imposes limits on the algorithmic options available to an implementation. "
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    ABSTRACT: We study and develop constraint preserving boundary conditions for the Newtonian magnetohydrodynamic equations and analyze the behavior of the numerical solution upon considering different possible options. We concentrate on both the standard ideal MHD system and the one augmented by a “pseudo potential” to control the divergence free constraint. We show how the boundary conditions developed significantly reduce the violations generated at the boundaries at the numerical level and how lessen their influence in the interior of the computational domain by making use of the available freedom in the equations.
    Computer Physics Communications 10/2008; 179(8-179):545-554. DOI:10.1016/j.cpc.2008.04.015 · 3.11 Impact Factor
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    • "Such simulations have only recently become possible. Duez et al. (2005) and Shibata & Sekiguchi (2005) have developed new codes to evolve the coupled set of Einstein-Maxwell-MHD equations self-consistently. Our two codes have since been used to simulate the evolution of magnetized HMNSs (Duez et al. 2006a,2006b), and implications for short GRBs have been investigated (Shibata et al. 2006). "
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    ABSTRACT: Black holes are popping up all over the place: in compact binary X-ray sources and GRBs, in quasars, AGNs and the cores of all bulge galaxies, in binary black holes and binary black hole-neutron stars, and maybe even in the LHC! Black holes are strong-field objects governed by Einstein's equations of general relativity. Hence general relativistic, numerical simulations of dynamical phenomena involving black holes may help reveal ways in which black holes can form, grow and be detected in the universe. To convey the state-of-the art, we summarize several representative simulations here, including the collapse of a hypermassive neutron star to a black hole following the merger of a binary neutron star, the magnetorotational collapse of a massive star to a black hole, and the formation and growth of supermassive black hole seeds by relativistic MHD accretion in the early universe.
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