A spectral method algorithm for numerical simulations of gravitational fields
arXiv:2011.10354 · doi:10.1088/1361-6382/abdd0b
Abstract
A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the Arnowitt-Deser-Misner (ADM) and the conformal Baumgarte-Shapiro-Shibata-Nakamura (BSSN) approach. The numerical code is based on the Fourier decomposition, accompanied by different filtering techniques. The role of the dealiasing, as well as the influence of the filter type, has been investigated. The algorithms have been stabilized via a novel procedure that controls self-consistently the regularity of the solutions. The accuracy of the model has been validated through standard testbeds, revealing that the filtered pseudo-spectral technique is among the most accurate approaches. Finally, the procedure has been stressed via black hole dynamics and a new strategy, based on hyperviscous dissipation that suppresses spurious boundary problems, has been proposed. The model represents a valid tool of investigation, particularly suitable for the inspection of small scale nonlinear phenomena in gravitational dynamics.
arXiv comment38 pages, 14 figures
References in corpus (68)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- The Dynamics of General Relativity
- First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- On the Numerical Integration of Einstein's Field Equations
- Evolutions in 3D numerical relativity using fixed mesh refinement
- The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
- Gauge conditions for long-term numerical black hole evolutions without excision
- The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
- New Formalism for Numerical Relativity
- Universal Interferometric Signatures of a Black Hole's Photon Ring
- The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project
- Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
- Conformal and covariant formulation of the Z4 system with constraint-violation damping
- Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
- Four-Body Effects in Globular Cluster Black Hole Coalescence
- Initial Data for Numerical Relativity
- Modeling the dynamics of tidally-interacting binary neutron stars up to merger
- Numerical simulation of orbiting black holes
- Magnetic field generation in fully convective rotating spheres
- Spectral Methods for Numerical Relativity
- On the final spin from the coalescence of two black holes
- Solving Einstein's Equations With Dual Coordinate Frames
- Effects of the microphysical Equation of State in the mergers of magnetized Neutron Stars With Neutrino Cooling
- THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
- Accurate black hole evolutions by fourth-order numerical relativity
- Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
- The Kerr Metric
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- An improved analysis of GW150914 using a fully spin-precessing waveform model
- Numerical relativity simulations of binary neutron stars
- GRChombo : Numerical Relativity with Adaptive Mesh Refinement
- All-sky search for gravitational-wave bursts in the first joint LIGO-GEO-Virgo run
- The Innermost Stable Circular Orbit of Binary Black Holes
- Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
- Toward standard testbeds for numerical relativity
- How loud are neutron star mergers?
- Foundations of multiple black hole evolutions
- Initial Data and Coordinates for Multiple Black Hole Systems
- Modeling non-thermal emission from the jet-launching region of M 87 with adaptive mesh refinement
- Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
- An Introduction to the Einstein Toolkit
- Hyperbolicity of the BSSN system of Einstein evolution equations
- Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
- Where do moving punctures go?
- On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
- Key Elements of Robustness in Binary Black Hole Evolutions using Spectral Methods
- BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
- Implementation of standard testbeds for numerical relativity
- Massively Parallel Simulations of Binary Black Hole Intermediate-Mass-Ratio Inspirals
- Conformal and covariant Z4 formulation of the Einstein equations: strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes
- Close encounters of three black holes
- Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity
- Long term black hole evolution with the BSSN system by pseudospectral methods
- Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
- Numerical simulations with a first order BSSN formulation of Einstein's field equations
- Construction of initial data for 3+1 numerical relativity
- BSSN in Spherical Symmetry
- Puncture Initial Data for Black-Hole Binaries with High Spins and High Boosts
- Stable 3-level leapfrog integration in numerical relativity
- Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
- Black hole critical behaviour with the generalized BSSN formulation
- Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests
- Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
- Numerical solutions to Einstein's equations in a shearing-dust Universe: a code comparison
- Numerical stability of the AA evolution system compared to the ADM and BSSN systems
- Hyperbolicity of Hamiltonian formulations in General Relativity
Cited by in corpus (6)
- PBH formation from spherically symmetric hydrodynamical perturbations: a review
- Lessons for adaptive mesh refinement in numerical relativity
- A high-order shock capturing discontinuous Galerkin-finite-difference hybrid method for GRMHD
- Extreme Gravitational Interactions in the Problem of Three Black Holes in General Relativity
- On the stability of covariant BSSN formulation
- Aliasing Instabilities in the Numerical Evolution of the Einstein Field Equations