General relativistic MHD large eddy simulations with gradient subgrid-scale model

Abstract

In several relativistic astrophysics scenarios, the understanding of the rich magnetohydrodynamics is hampered by the limitations set by the achievable numerical resolution. In these cases, it is a tremendous challenge to accurately simulate numerically all the relevant scales. We present how to study such systems by using large eddy simulations with a self-consistent subgrid-scale gradient model that we generalized to the special relativistic case in a previous work and now extend to the general relativistic case. Adapted from nonrelativistic scenarios, the so-called gradient model allows us to capture part of the effects of the hidden dynamics on the resolved scales, by means of a physically agnostic, mathematically based Taylor expansion of the nonlinear terms in the conservative evolution equations' fluxes. One of the main applications is the binary neutron star mergers, where the collision excites a nontrivial amplification at small spatial scales. Motivated by this scenario, we assess the validity of this approach in bounding-box simulations of the magnetic Kelvin-Helmholtz instability. Several resolutions and a broad range of scenarios are considered in order to carefully test the performance of the model under three crucial aspects: (i) highly curved backgrounds, (ii) jumps on the fluid density profiles, and (iii) strong shocks. The results suggest that our extension of the gradient subgrid-scale model to general relativistic magnetohydrodynamics is a promising approach for studying binary neutron star mergers and other relevant astrophysical scenarios.

Turbulent magnetic-field amplification in the first 10 milliseconds after a binary neutron star merger: Comparing high-resolution and large-eddy simulations

“…A more sophisticated alternative, based on the so-called gradient SGS model [41,42], has been proposed recently for Newtonian, special and general relativistic MHD, respectively in [43][44][45]. It was proven to have very good performance (in terms of capturing the magnetic amplification especially) in box simulations of the KHI, for a variety of initial conditions and resolutions, but it was not yet implemented in BNS mergers.…”

Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model

“…More simulations are needed to establish the degree to which systematic uncertainties due to turbulence will limit our ability to search for new physics, such as phase transitions, in multi-messenger observations of BNS mergers. The method we propose here could be and has been extended to the full-GRMHD equations [84,85]. Including GRMHD in our simulations will be crucial to capture also the large-scale effects due magnetic fields, such as jet launching [37,65], which are presently not included.…”

“…Similarly, the three-velocity v i is also a nonlinear function of the evolved coarse-grained quantities, so we would need to include a closure also for v i . These terms were treated in full generality in [84,85], to which we refer for the details. Here, we neglect these corrections, e.g., we assume Π = 0, because we expect them to be subdominant, since turbulence in the postmerger remnant is subsonic and subrelativistic, meaning that its character should be fully captured by τ ij .…”

“…More recently, a rigorous first-principles theory of relativistic turbulence that, among other things, strengthens the mathematical foundation for the GRLES method was proposed by Eyink and Drivas [83]. An extension of the method to GRMHD, taking into account also terms that we neglected in our initial formulation (more on this below) was proposed in [84,85]. Rosofsky and Huerta [86] proposed to use machine learning to calibrate subgrid turbulence models for 2D MHD.…”

Electromagnetic counterparts of compact binary mergers

“…To overcome this limitation, effective subgrid amplification methods have been proposed (e.g. Giacomazzo et al 2015;Viganò et al 2020).…”