Session G18: Numerical Relativity: Magnetohydrodynamics

Live

I will present our newly developed GRMHD code aimed to the study of compact binary mergers with finite temperature equations of state and neutrino emission. Numerical modeling of compact binaries is now one of the most important fields of study in theoretical astrophysics because it allows extracting physical information from the gravitational wave and electromagnetic signals by comparing simulations with observations. In the NS-NS and NS-BH cases, only a fully general relativistic treatment taking into account accurate magnetic field's evolution and microphysic's effects may give a complete picture of this scenario. I will summarize the main features of our code, namely: the evolution of a staggered vector potential that automatically satisfies the magnetic field's divergence-free condition; the general treatment for the NS Equation Of State allowing for the use of either analytical or tabulated one; a neutrino leakage scheme that provides a useful tool for the study of the post-merger phase. I will also present all the tests that we performed, including TOV taking into account temperature and electron fraction evolutions. Our future plan is to perform BNS merger simulations within the NASA TCAN 80NSSC18K1488 grant.   

Live

Spherical-like coordinates have many advantages when it comes to evolving systems that are approximately axially symmetric. This includes the remnants of compact-object mergers. However, the often severe Courant limitation associated with the origin and polar axis can make high-resolution simulations impractical. In this talk we describe two techniques for mitigating the Courant limitation using filtering algorithms   

Live

We present MHD simulations of the Papaloizou-Pringle Instability (PPI) in full GR. Our simulations are the first to explore the effects of BH spin and large disk masses on the development and saturation of the PPI. Disk-to-BH mass ratios range from \(\sim1/7\) to \(\sim2\). The black hole spin magnitudes range from \(0\) to \(0.7\), with spins both aligned and anti-aligned with the disk's orbital angular momentum. We discuss the dynamics and their astrophysical implications, focusing on multimessenger signatures and the detectability of GW signals by present and future GW observatories.   

Live

We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to systematically quantify the performance of neural network models to reproduce the physics of these complex simulations. We compare the performance of our neural networks with gradient models, which are extensively used in the extensively in the magnetohydrodynamic literature. Our findings indicate that neural networks significantly outperform gradient models at reproducing the effects of magnetohydrodynamics turbulence. To the best of our knowledge, this is the first exploratory study on the use of deep learning to learn and reproduce the physics of magnetohydrodynamics turbulence.   

Not Participating

We develop methods for simulation of multi-dimensional neutrino transport in nuclear astrophysics applications; e.g., core-collapse supernovae and binary neutron star mergers. The computational cost associated with simulations of these events is largely dominated by modeling the neutrino-matter coupling, and efficient solvers and implementations are needed for high-fidelity simulations. In the context of a multi-group two-moment model employing discontinuous Galerkin phase space discretization and implicit-explicit time integration\footnote{Chu et al. 2019, {\it JCP}, {\bf 389}, 62}, we present results from a comparison of various nonlinear solvers for four-momentum and lepton exchange due to emission and absorption, scattering, and pair processes. We also discuss preliminary results from porting these algorithms to GPUs.   

Not Participating

Numerical simulations in GR hydrodynamics and MHD are almost universally carried out with equations written in conservative form. This allows robust handling of shocks and other discontinuities in the flow. To enforce boundary conditions and handle shocks, it is useful to be able to transform back and forth between the conservative variables and the characteristic variables. However, the required characteristic decomposition for GRMHD has proved too complicated to derive in the usual Eulerian frame used in simulations. One method that has been tried transforms the variables instead of the equations, starting with the relatively simple decomposition in the comoving frame. However, this method is extremely complicated and also does not seem able to handle both the left and right eigenvectors in full GR. To handle this problem, we introduce a new kind of transformation that is only quasi-invertible. It leads to simpler forms for the hydro case than those in the literature, and may finally make more robust methods tractable for GRMHD.   

Not Participating

Relativistic MHD is often used to model astrophysical systems with magnetic fields, such as binary neutron star mergers and accretion disks. One challenge in solving these equations numerically is the wide range of length scales that must be adequately resolved, especially to capture the small-scale dynamics that affect the large-scale magnetic field. Dendro-GR is a new computational platform for relativistic astrophysics that uses a highly efficient parallel octree with Wavelet Adaptive Multi-Resolution (WAMR) to enable large, multi-scale simulations. This code is being used to study binary black hole mergers. We are adding relativistic MHD to Dendro-GR with the ultimate aim of evolving binary neutron stars. We report on the progress of this project and present some initial results from tests with simpler systems, such as magnetized flows in flat spacetime and GRB outflows.