Gradient subgrid-scale model for relativistic MHD large-eddy simulations

Abstract

MHD turbulence is likely to play an important role in several astrophysical scenarios where the magnetic Reynolds is very large. Numerically, these cases can be studied efficiently by means of Large Eddy Simulations, in which the computational resources are used to evolve the system only up to a finite grid size. The resolution is not fine enough to capture all the relevant small-scale physics at play, which is instead effectively modeled by a set of additional terms in the evolution equations, dubbed as sub-grid-scale model. Here we extend such approach, commonly used in nonrelativistic/non-magnetic/incompressible fluid dynamics, applying the so-called gradient model to a general set of balance-law equations, that includes the relevant case in which a non-trivial inversion of conserved to primitive fields is needed. In particular, we focus on the relativistic compressible ideal MHD scenario, providing for the first time (and for any equation of state) all the additional subgrid-scale terms. As an application, we consider box simulations of the relativistic Kelvin-Helmholtz instability, which is also the first mechanism responsible for the magnetic field amplification in binary neutron star mergers and cannot yet be fully captured by the finest-grid and longest simulations available. The performance of our model is numerically assessed by comparing it to the residuals arising from the filtering of high-resolution simulations. We find that the model can fit very well those residuals from resolutions a few times higher. Although the application shown here explicitly considers the Minkowski metric, it can be directly extended to general relativity, thus settling the basis to implement the gradient sub-grid model in a GRMHD binary merger. Our results suggest that this approach will be potentially able to unveil much better the small-scale dynamics achievable in full GRMHD simulations.

Comparison of momentum transport models for numerical relativity

“…1 However, "not covariant" does not necessarily mean "not valid." Similar points are made by Carrasco et al [22] with regard to their relativistic subgrid code. Since theirs is a large-eddy code, they also point out that discretization for finite differencing itself violates covariance in the same way and to a similar degree.…”

“…In what we will call "large-eddy simulations," it is assumed that a significant portion of the inertial range is resolved, and subgrid stress terms are computed as an extrapolation of the character of resolved turbulence to subgrid scales (e.g., [18][19][20][21]). An example of such methods is the gradient model that has recently been adapted to relativistic magnetohydrodynamics by Carrasco, Viganò, and Palenzuela [22] (see also [23]). The subgrid dynamo term of Giacomazzo et al [4] might also fit into this category, because the field growth is stopped when the magnetic energy density approaches an estimate of the subgrid turbulent kinetic energy density.…”

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.…”