Aliasing instabilities in the numerical evolution of the Einstein field equations

Self Cite

We study the three-body problem going from Newtonian mechanics to general relativity. In the classical case, we model the interactions in a typical chaotic configuration, identifying Extreme Gravitational Interactions (EGIs), namely transients in which the system manifests complex, highly-energetic dynamics. We then concentrate on the main part of the work, by selecting these EGIs as initial data for the general relativistic case, and performing a campaign of numerical relativity simulations. To provide a comprehensive menu of cases, we investigate different global configurations. By comparing with the more ``quiet'' two-body inspiral, we observe strong nonlinear emission of gravitational waves. The multi-body signals have been inspected by employing both Fourier and wavelet analyses, showing net differences among the global configurations. The wavelet analysis reveals the reminiscence of the EGIs in the three black holes problem. Such a survey of simulations might be a guide for future observations.

Section: The Sfinge Codementioning

confidence: 99%

“…Terms of the type ν n ∇ n f, where ν n is a dissipative numerical coefficient, can indeed strongly dissipate very smallscale ripples and noise. See [36,56] for more technical details on the procedure.…”

Section: The Sfinge Codementioning

confidence: 99%

Extreme gravitational interactions in the problem of three black holes in general relativity

Imbrogno

Meringolo

Servidio

2023

Self Cite

“…A unique feature of SpecCosmo's design is that all derivatives are calculated outside of the main loops making it possible to choose the differencing method at run-time. For this work, we utilize a Fourier pseudospectral method along with a 2/3 dealiasing scheme [8][9][10][11]. Because this is fundamentally a turbulence simulation, we use periodic boundary conditions.…”

Section: Numerical Codementioning

confidence: 99%

Initial conditions for GRMHD simulations of electroweak and QCD phase transitions in the early Universe

Barrera,

Warren,

Garrison

2023

This work identifies the initial conditions of GRMHD simulations of both the Electroweak and Quantum Chromodynamic phase transitions. Each phase transition has a well known vacuum expectation value associated with it, which will be the starting point for each calculation. Energy, temperature, scale factor, Hubble Parameter, time, thermal degrees of freedom, dark matter density, regular matter density and radiation density are the nine parameters that will be found for each phase transition. Some of the parameters are needed to calculate others, and some of the parameters are direct inputs required by our computer code. In addition, the magnitude of velocity variations as well as density and temperature perturbations is found using numerical simulations. The data generated by these inputs combined with the evolution equations can be analyzed to determine if the simulation conforms to the FRW model and whether or not the hypothesized values are accurate.

“…High-order pseudospectral methods have proven extremely useful in producing a large number of long and accurate gravitational waveforms from binary black hole merger simulations [17][18][19][20][21][22][23][24][25] as well as other applications in relativistic astrophysics [26][27][28][29][30][31]. Since binary inspirals emit gravitational radiation, the numerical solution in most of the computational domain is smooth but non-constant, and so high-order methods are preferable.…”

Section: Introductionmentioning

confidence: 99%

A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD

Deppe¹,

Hébert²,

Kidder³

et al. 2022

We present a discontinuous Galerkin (DG)–finite difference (FD) hybrid scheme that allows high-order shock capturing with the DG method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited DG candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust FD methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the DG and FD solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1D, 2D, and 3D relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.