Relativistic MHD with adaptive mesh refinement

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the had computational infrastructure for distributed adaptive mesh refinement.

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“…Additional information can be found in our previous work [24,25] as well as in general review articles [29,30].…”

Section: B Perfect Fluid Equationsmentioning

confidence: 99%

Simulating binary neutron stars: Dynamics and gravitational waves

et al. 2008

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“…An additional direction of research has been represented by the inclusion of dissipative effects, namely non-ideal resistive magnetohydrodynamics, with encouraging results (Komissarov 2007;Palenzuela et al 2009;Dumbser & Zanotti 2009;Zenitani et al 2010;Takamoto & Inoue 2011;Bucciantini & Del Zanna 2013). Moreover, high order numerical schemes have also been pursued (Del Zanna et al 2003;Anderson et al 2006), while simulations of multi-fluids in RMHD are emerging as a new frontier (Zenitani et al 2009;Barkov et al 2014). Finally, Adaptive Mesh Refinement (AMR) within RMHD codes has been also considered (Balsara 2001b;Neilsen et al 2006;Etienne et al 2010;Mignone et al 2012;Keppens et al 2012; and it is an active field of research.…”

Section: Introductionmentioning

confidence: 99%

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

Zanotti

Fambri

Dumbser

2015

Mon. Not. R. Astron. Soc.

114

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We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an arbitrary order of accuracy in both space and time, (ii) an a posteriori subcell finite volume limiter that is activated to avoid spurious oscillations at discontinuities without destroying the natural subcell resolution capabilities of the DG finite element framework and finally (iii) a space-time adaptive mesh refinement (AMR) framework with time-accurate local time-stepping.The divergence-free character of the magnetic field is instead taken into account through the so-called "divergence-cleaning" approach. The convergence of the new scheme is verified up to 5 th order in space and time and the results for a set of significant numerical tests including shock tube problems, the RMHD rotor and blast wave problems, as well as the Orszag-Tang vortex system are shown. We also consider a simple case of the relativistic Kelvin-Helmholtz instability with a magnetic field, emphasizing the potential of the new method for studying turbulent RMHD flows. We discuss the advantages of our new approach when the equations of relativistic MHD need to be solved with high accuracy within various astrophysical systems.

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“…Often mesh refinement [51,[80][81][82] is used not only to increase the resolution in regions of interest but also to move the region of higher resolution along with the object. In this approach, as the NSs move through the grid and get close to the current edge of the high resolution grid, new grid points are created and populated with data interpolated from the coarse grid in front of the NS and no longer needed points are destroyed once the NS has passed.…”

Section: Mesh Refinementmentioning

confidence: 99%

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

et al. 2016

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We present results on the inspiral, merger, and post-merger evolution of a neutron star -neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for ≈ 22 orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.

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Relativistic MHD with adaptive mesh refinement

Cited by 99 publications

References 57 publications

Simulating binary neutron stars: Dynamics and gravitational waves

Simulating binary neutron stars: Dynamics and gravitational waves

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

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