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.

Oscillations of highly magnetized non-rotating neutron stars

“…Simulations. Simulations are performed with our code Gmunu [75][76][77][78] . For each of the 12 equilibrium models, we execute Gmunu three times, once for each initial perturbation function.…”

“…A more rigorous approach to compute strongly magnetized equilibrium models is recently presented and demonstrated by an opensource code XNS 3,[64][65][66][67][68][69][70][71][72][73][74] . Moreover, the GRMHD code Gmunu [75][76][77][78] allows us to robustly evolve NSs in dynamical spacetime even with extreme magnetic fields of 10 15−17 G. With these powerful tools in hand, we are now in a much better position to systematically investigate the oscillation modes of magnetized NSs.…”

General-relativistic Radiation Transport Scheme in Gmunu. I. Implementation of Two-moment-based Multifrequency Radiative Transfer and Code Tests

“…To consistently solve the metric equations, the contribution of the radiations must be taken into account as well. This can be done simply by including the 3 + 1 decomposed source terms for radiation into our metric solver (Cheong et al 2020(Cheong et al , 2021…”

“…Similar to the standard "atmosphere" treatment for rest-mass density ρ in hydrodynamical simulation (e.g., Cheong et al 2020Cheong et al , 2021, we enforce the nonnegativity of the energy density  . In particular, we define a minimum allowed distribution function f min and a threshold f thr , where…”

An Extension of Gmunu: General-relativistic Resistive Magnetohydrodynamics Based on Staggered-meshed Constrained Transport with Elliptic Cleaning

“…If the electric field E i and the magnetic field B i are given, the conserved variables q can then be transformed into primitive variables (ρ, Wv i , p) using the method for general-relativistic hydrodynamics described in Cheong et al (2020Cheong et al ( , 2021 by removing the electromagnetic part.…”