Gmunu: Toward multigrid based Einstein field equations solver for general-relativistic hydrodynamics simulations

Abstract

We present a new open-source axisymmetric general relativistic hydrodynamics code Gmunu (General-relativistic multigrid numerical solver) which uses a multigrid method to solve the elliptic metric equations in the conformally flat condition (CFC) approximation on a spherical grid. Most of the existing relativistic hydrodynamics codes are based on formulations which rely on a free-evolution approach of numerical relativity, where the metric variables are determined by hyperbolic equations without enforcing the constraint equations in the evolution. On the other hand, although a fully constrained-evolution formulation is theoretical more appealing and should lead to more stable and accurate simulations, such an approach is not widely used because solving the elliptic-type constraint equations during the evolution is in general more computationally expensive than hyperbolic free-evolution schemes. Multigrid methods solve differential equations with a hierarchy of discretizations and its computational cost is generally lower than other methods such as direct methods, relaxation methods, successive over-relaxation. With multigrid acceleration, one can solve the metric equations on a comparable time scale as solving the hydrodynamics equations. This would potentially make a fully constrained-evolution formulation more affordable in numerical relativity simulations. As a first step to assess the performance and robustness of multigrid methods in relativistic simulations, we develop a hydrodynamics code that makes use of standard finite-volume methods coupled with a multigrid metric solver to solve the Einstein equations in the CFC approximation. In this paper, we present the methodology and implementation of our code Gmunu and its properties and performance in some benchmarking relativistic hydrodynamics problems.

References in corpus (32)

• Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals from neutron-star mergers
• Relativistic simulations of rotational core collapse. II. Collapse dynamics and gravitational radiation
• Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
• Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers
• Three-Dimensional Simulations of Neutrino-Driven Core-Collapse Supernovae from Low-Mass Single and Binary Star Progenitors
• Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars
• Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests
• General-covariant evolution formalism for Numerical Relativity
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• Revealing the high-density equation of state through binary neutron star mergers
• The Dynamics of Neutrino-Driven Supernova Explosions after Shock Revival in 2D and 3D
• Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
• Implementation of a simplified approach to radiative transfer in general relativity
• Conformally Flat Smoothed Particle Hydrodynamics: Application to Neutron Star Mergers
• Axisymmetric equilibrium models for magnetized neutron stars in General Relativity under the Conformally Flat Condition
• Nonlinear Pulsations in Differentially Rotating Neutron Stars: Mass-Shedding-Induced Damping and Splitting of the Fundamental Mode
• Three Dimensional Numerical General Relativistic Hydrodynamics I: Formulations, Methods, and Code Tests
• Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
• "Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
• Waveless Approximation Theories of Gravity
• GRMHD in axisymmetric dynamical spacetimes: the X-ECHO code
• Rotating Collapse of Stellar Iron Cores in General Relativity
• General relativistic neutron stars with twisted magnetosphere
• General relativistic models for rotating magnetized neutron stars in conformally flat spacetime
• Conformal Thin-Sandwich Solver for Generic Initial Data
• General relativistic hydrodynamics in curvilinear coordinates
• Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits
• Initial data for binary neutron stars with adjustable eccentricity
• R-mode oscillations of rapidly rotating barotropic stars in general relativity: Analysis by the relativistic Cowling approximation
• The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations
• Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
• Disk formation in the collapse of supramassive neutron stars

Cited by in corpus (22)

• Gmunu: Paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical spacetimes
• General-relativistic radiation transport scheme in $\text{Gmunu}$ I: Implementation of two-moment based multi-frequency radiative transfer and code tests
• Gamma-ray bursts and kilonovae from the accretion-induced collapse of white dwarfs
• An extension of Gmunu: General-relativistic resistive magnetohydrodynamics based on staggered-meshed constrained transport with elliptic cleaning
• Multimessenger Emission from the Accretion Induced Collapse of White Dwarfs
• Energy-dependent and energy-integrated two-moment general-relativistic neutrino transport simulations of hypermassive neutron star
• Oscillations of Highly Magnetized Non-rotating Neutron Stars
• A hybrid approach to long-term binary neutron-star simulations
• General-relativistic radiation transport scheme in Gmunu II: Implementation of novel microphysical library for neutrino radiation -- Weakhub
• Influence of neutrino-electron scattering and neutrino-pair annihilation on hypermassive neutron star
• High angular momentum hot differentially rotating equilibrium star evolutions in conformally flat spacetime
• General-relativistic resistive-magnetohydrodynamics simulations of self-consistent magnetized rotating neutron stars
• Formation of a magnetized hybrid star with a purely toroidal field from phase-transition-induced collapse
• Long-term impact of the magnetic-field strength on the evolution and electromagnetic emission by neutron-star merger remnants
• Gravitational wave signatures from the phase-transition-induced collapse of a magnetized neutron star
• Hyperaccreting Neutron Stars inside Massive Envelopes: The Implausibility of Thorne-Żytkow Objects
• Toward First-Principles Multi-Messenger Predictions: Coupling Nuclear Networks with GR Radiation-MHD in {\tt Gmunu}
• Gamma-ray Signatures of r-Process Radioactivity from the Collapse of Magnetized White Dwarfs
• Revisiting the apparent horizon finding problem with multigrid methods
• MIR: a general-relativistic resistive-magneto-hydrodynamic code to study the effect of resistivity in Neutron Star dynamics
• Fundamental modes of rotating neutron stars with various degrees of differential rotation in dynamical spacetimes
• Gravitational-wave asteroseismology with f-modes from neutron star binaries at the merger phase