Structure of rotating self-gravitating figures of equilibrium in Newtonian gravity and general relativity with an emphasis on neutron stars

Studio di modelli numerici per la costruzione di configurazione di equilibrio di stelle in rotazione rapida sia in gravità Newtoniana che in Relatività Generale. Presentazione del mio codice Newtoniano e applicazione dei risultati in campo relativistico a problemi astrofisicamente interessanti

Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit

We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamic (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. We validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.Fil: Mewes, Vassilios. Rochester Institute Of Technology; Estados UnidosFil: Zlochower, Yosef. Rochester Institute Of Technology; Estados UnidosFil: Campanelli, Manuela. Rochester Institute Of Technology; Estados UnidosFil: Baumgarte, Thomas W.. Bowdoin College; Estados UnidosFil: Etienne, Zachariah B.. West Virginia University; Estados UnidosFil: Lopez Armengol, Federico Gaston. Rochester Institute Of Technology; Estados Unidos. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Cipolletta, Federico. Rochester Institute Of Technology; Estados Unido

Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition timestep limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double FFT filter and implementing it within the fully MPI-parallelized SphericalNR framework in the Einstein Toolkit. We demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the timestep significantly compared to unfiltered simulations.Comment: 15 pages, 13 figures, revtex4-

Spritz: General Relativistic Magnetohydrodynamics with Neutrinos

We here present a new version of the publicly available general relativistic magnetohydrodynamic (GRMHD) code $\texttt{Spritz}$, which now includes an approximate neutrino leakage scheme able to handle neutrino cooling and heating. The leakage scheme is based on the publicly available $\texttt{ZelmaniLeak}$ code, with a few modifications in order to properly work with $\texttt{Spritz}$. We discuss the involved equations, physical assumptions, and implemented numerical methods, along with a large battery of general relativistic tests performed with and without magnetic fields. Our tests demonstrate the correct implementation of the neutrino leakage scheme, paving the way for further improvements of our neutrino treatment and the first application to magnetized binary neutron star mergers. We also discuss the implementation in the $\texttt{Spritz}$ code of high-order methods for a more accurate evolution of hydrodynamical quantities.Comment: 34 pages, 16 figures. The code is available on Zenodo as version 1.1.0 at https://doi.org/10.5281/zenodo.3689751. Initial data and equation of state used in this paper can be downloaded from https://drive.google.com/drive/folders/1kGBRW_AhKjHrOi76uXXPRyaCc1BfgqQN?usp=sharin

Next-generation HPC models for future Rotorcraft applications

Rotorcraft technologies pose great scientific and industrial challenges for numerical computing. As available computational resources approach the exascale, finer scales and therefore more accurate simulations of engineering test cases become accessible. However, shifting legacy workflows and optimizing parallel efficiency and scalability of existing software on new hardware is often demanding. This paper reports preliminary results in CFD and structural dynamics simulations using the T106A Low Pressure Turbine (LPT) blade geometry on Leonardo S.p.A.'s davinci-1 high-performance computing (HPC) facility. Time to solution and scalability are assessed for commercial packages Ansys Fluent, STAR-CCM+, and ABAQUS, and the open-source scientific computing framework PyFR. In direct numerical simulations of compressible fluid flow, normalized time to solution values obtained using PyFR are found to be up to 8 times smaller than those obtained using Fluent and STAR-CCM+. The findings extend to the incompressible case. All models offer weak and strong scaling in tests performed on up to 48 compute nodes, each with 4 Nvidia A100 GPUs. In linear elasticity simulations with ABAQUS, both the iterative solver and the direct solver provide speedup in preliminary scaling tests, with the iterative solver outperforming the direct solver in terms of time-to-solution and memory usage. The results provide a first indication of the potential of HPC architectures in scaling engineering applications towards certification by simulation, and the first step for the Company towards the use of cutting-edge HPC toolkits in the field of Rotorcraft technologies

Collapse of spherical charged anisotropic fluid spacetimes

A class of spherical collapsing exact solutions with electromagnetic charge is derived. This class of solutions -- in general anisotropic -- contains however as a particular case the charged dust model already known in literature. Under some regularity assumptions that in the uncharged case give rise to naked singularities, it is shown that the process of shell focusing singularities avoidance -- already known for the dust collapse -- also takes place here, determing shell crossing effects or a completely regular solution.Comment: 13 pages, 2 figures. Version to appear on Class Quantum Gra

Addition of tabulated equation of state and neutrino leakage support to IllinoisGRMHD

We have added support for realistic, microphysical, finite-temperature equations of state (EOS) and neutrino physics via a leakage scheme to IllinoisGRMHD, an open-source GRMHD code for dynamical spacetimes in the Einstein Toolkit. These new features are provided by two new, NRPy+-based codes: NRPyEOS, which performs highly efficient EOS table lookups and interpolations, and NRPyLeakage, which implements a new, AMR-capable neutrino leakage scheme in the Einstein Toolkit. We have performed a series of strenuous validation tests that demonstrate the robustness of these new codes, particularly on the Cartesian AMR grids provided by Carpet. Furthermore, we show results from fully dynamical GRMHD simulations of single unmagnetized neutron stars, and magnetized binary neutron star mergers. This new version of IllinoisGRMHD, as well as NRPyEOS and NRPyLeakage, is pedagogically documented in Jupyter notebooks and fully open source. The codes will be proposed for inclusion in an upcoming version of the Einstein Toolkit.Comment: 20 pages, 9 figures. v2 matches PRD versio

Handing off the outcome of binary neutron star mergers for accurate and long-term post-merger simulations

We perform binary neutron star (BNS) merger simulations in full dynamical general relativity with IllinoisGRMHD, on a Cartesian grid with adaptive-mesh refinement. After the remnant black hole has become nearly stationary, the evolution of the surrounding accretion disk on Cartesian grids over long timescales (1s) is suboptimal, as Cartesian coordinates over-resolve the angular coordinates at large distances, and the accreting plasma flows obliquely across coordinate lines dissipating angular momentum artificially from the disk. To address this, we present the Handoff, a set of computational tools that enables the transfer of general relativistic magnetohydrodynamic (GRMHD) and spacetime data from IllinoisGRMHD to HARM3D, a GRMHD code that specializes in modeling black hole accretion disks in static spacetimes over long timescales, making use of general coordinate systems with spherical topology. We demonstrate that the Handoff allows for a smooth and reliable transition of GRMHD fields and spacetime data, enabling us to efficiently and reliably evolve BNS dynamics well beyond merger. We also discuss future plans, which involve incorporating advanced equations of state and neutrino physics into BNS simulations using the \handoff approach