Session B16: Numerical Methods

Magnetized neutron stars mergers with neutrinos

We extend the MHDuet code to model compact object mergers described by realistic, temperature-dependent equations of state with neutrinos coupled to fully nonlinear gravitational magnetohydrodynamics (GRMHD) that uses a large-eddy-simulation (LES) subgrid model.   

BlackHoles@Home

BlackHoles@Home is a new, highly efficient numerical relativity code that fits binary black hole (BBH) simulations on consumer desktops. Its extreme efficiency enables the general public to participate in the creation of enormous and highly accurate BBH gravitational waveform catalogs, for the benefit of gravitational wave science. Over the past year the BlackHoles@Home infrastructure has been rewritten to facilitate simulations of not only the long BBH inspiral, but also its merger---both with improved efficiency and reliability. Further the Einstein Toolkit has been recast as an open-source library, which we leverage for state-of-the-art horizon diagnostics in BlackHoles@Home. An update on the volunteer computing/citizen science project will also be provided.   

Calculating the Vorticity of Spacetime in SpECTRE

Near the time of merger, numerical relativity is necessary to model gravitational waves from merging black holes and neutron stars, because near the time of merger all analytic approximations fail. SpECTRE is a next-generation numerical-relativity code being developed by the Simulating eXtreme Spacetimes (SXS) collaboration that will calculate these gravitational waves with high accuracy by scaling to large numbers of compute cores. Simulations of merging black holes yield not only the emitted gravitational waves but also the nonlinear dynamics of the strongly curved spacetime. Tendicity (a measure of how curvature stretches and squeezes an observer through tides) and vorticity (a measure of how curvature twists an observer through differential frame dragging) are useful tools for gaining physical insight into the behavior of curved spacetimes. Mathematically, tendicity and vorticity follow from the electric and magnetic parts of the Weyl curvature tensor, respectively. In this talk, I will discuss implementing and testing a calculation of the magnetic part of the Weyl tensor in SpECTRE, with the goal of using it to help explore the behavior of warped spacetime in SpECTRE’s high-accuracy simulations of binary black holes.   

A spherical black hole gauge transformation for modeling rapidly spinning black holes with SpECTRE

SpECTRE is a new numerical-relativity code (currently under development) that will calculate the gravitational waves emitted by colliding black holes with unprecedented accuracy, which will help scientists interpret observations from next-generation gravitational-wave detectors. It can achieve high accuracy in part through using novel techniques to scale to hundreds of thousands of compute cores—far more than typical numerical-relativity codes can efficiently use.  Modeling rapidly spinning binary black holes with high accuracy is especially challenging, in part because. the conventional description of a rotating black hole uses coordinates in which the horizon (surface of the black hole) is oblate. I will discuss the implementation in SpECTRE of the coordinate transformation recently proposed by Chen, Deppe, Kidder, and Teukolsky (doi:10.1103/PhysRevD.104.084046) that ensures that the horizon is spherical, even when the black hole is spinning nearly as rapidly as possible. These coordinates are better adapted to the underlying symmetry; using them requires fewer grid points to simulate rapidly spinning black-hole spacetimes accurately.   

CurviGiRaFFE: A new code for modeling magnetospheres of compact object binaries

CurviGiRaFFE is an in-development, dynamical-spacetime GRFFE code aimed at studying the magnetospheres of compact object binaries. Unlike its parent codes, IllinoisGRMHD and GiRaFFE, CurviGiRaFFE does not require use of Cartesian AMR grids, instead leveraging NRPy+ to solve the GRFFE equations in dynamical spacetimes on highly efficient bispherical-like coordinate grids. These grids, composed of overlapping spherical-like and Cartesian-like grid patches, exploit near-symmetries in binary compact object spacetimes reducing memory overhead by orders of magnitude over Cartesian AMR. This efficiency gain will enable CurviGiRaFFE to model interacting compact binary magnetospheres on high-end, consumer-grade desktop computers, so the vast parameter space of magnetosphere configurations can be explored with minimal computational expense. I will report on CurviGiRaFFE’s covariant GRFFE formulation and preliminary code test results.   

NRPyElliptic: A Fast Hyperbolic Relaxation Solver for Numerical Relativity

NRPyElliptic is a new elliptic solver for numerical relativity (NR) built on the NRPy+ infrastructure. As its first application, it sets up conformally flat, binary puncture initial data on prolate-spheroidal-like grids, similar to the widely used TwoPunctures code. However, unlike TwoPunctures NRPyElliptic employs a hyperbolic relaxation scheme, whereby an elliptic equation is transformed into a hyperbolic equation. Our hyperbolic relaxation scheme has new performance enhancements that speed up the solver by orders of magnitude over the original approach, making it fast enough to generate compact binary initial data for NR. We report on current efforts to make NRPyElliptic compatible with the BlackHoles@Home multi-patch grid structure and extend the solver to generate other types of initial data. Our code has been developed as an Einstein Toolkit thorn and as a stand-alone code, both of which are documented in pedagogical Jupyter notebooks.   

A numerical laboratory for non-linear black hole perturbation theory

The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio. To facilitate a comparison between the two, we derive several results of linear perturbation theory in coordinates which may be adopted in numerical work. Firstly, we address the questions: for an initial configuration of a massless scalar field, what is the amplitude of the excited quasinormal mode (QNM) for any observer outside outside the event horizon, and furthermore what is the resulting tail contribution? We then present an implementation of the dual foliation generalized harmonic gauge (DF-GHG) formulation within our pseudospectral code 'bamps'. The formalism promises to give greater freedom in the choice of coordinates that can be used in numerical relativity. As a specific application we focus here on the treatment of black holes in spherical symmetry. Existing approaches to black hole excision in numerical relativity are susceptible to failure if the boundary fails to remain outflow. We present a method, called DF-excision, to avoid this failure. We compare the results of DF-excision with a naive setup and show that DF-excision proves reliable even when the previous approach fails. Finally, we use DF-excision and DF-GHG to perform fully non-linear simulations of a massless scalar field minimally coupled to general relativity using coordinates which are analogous to the Kerr-Schild coordinates from the linear setting. We perform a detailed analysis comparing the results of the non-linear simulations and the linear simulations and perform modeling of the non-linear time series data using several machine learning algorithms and compare their performance against each other.   

The current status of the Nmesh code

We give an introduction to the new Nmesh code, which is intended to efficiently run on large supercomputers. The aim of Nmesh is to solve challenging relativistic astrophysics problems such as binary neutron star or black hole mergers. The principal spatial discretization used in Nmesh is based on a discontinuous Galerkin (DG) method. However, we can also switch to finite difference (FD) or finite volume (FV) methods when needed in certain regions. To treat matter (e.g. neutron stars) we have implemented the evolution equations for general relativistic hydrodynamics. These can be coupled to the evolution equations for gravity. We are currently investigating three different gravity evolution systems, the generalized harmonic system, a first order version of the Z4 system, as well as a new system that we intend to use to evolve black holes using the moving puncture formalism. We will describe the current capabilities of our code and show some examples.   

The impact of numerical and algorithmic choices on the physical outcomes of GRMHD simulations of binary neutron star mergers

General-relativistic magnetohydrodynamics (GRMHD) simulations are crucial to understanding the physics of binary neutron star (BNS) mergers. However, some of the physically relevant observables in BNS mergers simulations — such as the gravitational wave signal in the inspiral phase and the lifetime of the hypermassive neutron star remnant — seem to depend on apparently irrelevant numerical and algorithmic choices.

In this talk, I will briefly introduce two GRMHD codes, namely Spritz and IllinoisGRMHD, and I will outline the relevant differences in the way they solve the GRMHD equations and in some numerical choices they adopt. Then I will present a set of BNS merger simulations, each performed with both codes, and I will discuss the differences in the physical outcomes of the runs depending on which of the two codes is chosen to perform them. Finally, I will try to link the differences in the physical observables coming from the simulations to some differences in numerical and/or algorithmic choices of each of the two codes.