Session G16: Methods of Numerical Relativity

Live

I will discuss a numerical implementation of the recently introduced modified generalized harmonic (MGH) formulation to numerically evolve the equations of motion of Einstein-scalar-Gauss-Bonnet (ESGB) gravity. In the MGH formulation ESGB gravity--along with all other "Horndeski" scalar-tensor gravity theories--has a well-posed initial value problem, which allows for the exact (numerical) solution of the equations of motion in regimes of astrophysical and cosmological interest. I will discuss binary black hole mergers in ESGB gravity using the MGH formulation; time permitting I will discuss potential uses of the MGH formulation in the numerical evolution of other scalar tensor gravity theories in cosmological spacetimes as well.   

Live

We present on progress investigating stability and maximal compactness of relativistic boson stars with non-linear potential. It has been shown that there exist relativistic boson stars so compact that they possess bound circular null geodesics, however a conjecture by Keir suggests that such stars are dynamically unstable in the spherically symmetric case. We test the conjecture and investigate the stability bounds of the boson stars.   

Live

I present the solver for linear and nonlinear elliptic partial differential equations for SpECTRE, the next-generation numerical relativity code currently in development by the SXS collaboration. The solver combines nodal discontinuous Galerkin methods and task-based parallelism to target challenging elliptic problems in numerical relativity and beyond. In particular, I report on first results solving for black-hole binary and neutron-star binary initial data using our new numerical technology and I demonstrate the code's ability to scale to the capacity of the Minerva supercomputer at AEI Potsdam.   

Live

We provide an update on the development of adaptive mesh refinement within SpECTRE (https://github.com/sxs-collaboration/spectre), an open-source relativistic astrophysics code that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers, while making efficient use of the largest supercomputers.   

Live

We present a new positivity-preserving adaptive-order method that combines discontinuous Galerkin and finite-difference schemes in a way that ensures physical realizability of the solution (e.g. positive density and pressure). The method is designed to preserve physical realizability during both reconstruction and time evolution. The idea is to start with an unlimited high-order discontinuous Galerkin method and fall back to a novel adaptive-order finite-difference scheme if the discontinuous Galerkin solution is not physically realizable. We will present a preliminary test result of our new robust adaptive-order method. The ultimate goal is to apply these methods to relativistic (magneto)hydrodynamics, such as simulations of binary neutron stars and accretion onto a black hole.   

Live

Dendro-GR is a new computational platform for challenging problems in numerical relativity. Dendro-GR uses conventional numerical methods for solving the Einstein equations and the relativistic fluid equations on a platform designed for massively parallel computing. Dendro-GR includes non-uniform grids, wavelet-based adaptive mesh refinement, and tools for symbolic code generation. This talk will review the features of Dendro-GR and its performance, as well as recent results with binary black hole mergers and perfect fluids.   

Live

We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of simulations of the magnetized Kelvin-Helmholtz instability (KHI). We produce simulations at different resolutions to systematically quantify the performance of neural network models to reproduce the physics of these complex simulations. We then implement these deep learning models in low resolution KHI simulations to examine their ability to reproduce the magnetic field amplification observed at high resolutions. We discuss the feasibility of using such models to reproduce the physics of magnetohydrodynamics turbulence in numerical relativity simulations of binary neutron star mergers.   

Live

We present the first nonlinear numerical solutions to the relativistic Navier-Stokes (RNS) equations recently proposed by Bemfica, Disconzi, Noronha, and Kovtun. These equations describe the dynamics of a heat-conducting, viscous relativistic fluid, and generalize the relativistic Euler equations governing perfect fluids. To serve as a first step toward the incorporation of the RNS equations into astrophysics simulations, we outline a scheme capable of solving the equations numerically, and solve them in 4D Minkowski spacetime for a fluid with an underlying conformal symmetry. We conclude by comparing the RNS solutions with those from the Mueller-Israel-Stewart (MIS) formalism, which has been successfully used to model the quark-gluon plasma formed in heavy ion collisions.