Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

Abstract

Performing accurate large eddy simulations in compressible, turbulent magnetohydrodynamics is more challenging than in non-magnetized fluids due to the complex interplay between kinetic, magnetic and internal energy at different scales. Here we extend the sub-grid-scale gradient model, so far used in the momentum and induction equations, to account also for the unresolved scales in the energy evolution equation of a compressible ideal MHD fluid with a generic equation of state. We assess the model by considering box simulations of the turbulence triggered across a shear layer by the Kelvin-Helmholtz instability, testing cases where the small-scale dynamics cannot be fully captured by the resolution considered, such that the efficiency of the simulated dynamo effect depends on the resolution employed. This lack of numerical convergence is actually a currently common issue in several astrophysical problems, where the integral and fastest-growing-instability scales are too far apart to be fully covered numerically. We perform a-priori and a-posteriori tests of the extended gradient model. In the former, we find that, for many different initial conditions and resolutions, the gradient model outperforms other commonly used models in terms of correlation with the residuals coming from the filtering of a high-resolution run. In the second test, we show how a low-resolution run with the gradient model is able to quantitatively reproduce the evolution of the magnetic energy (the integrated value and the spectral distribution) coming from higher-resolution runs. This extension is the first step towards the implementation in relativistic magnetohydrodynamics.

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

“…times. This behavior on the magnetic energy spectra of LES was also found in our bounding-box simulations [43][44][45].…”

“…However, finite-difference numerical methods are usually more dissipative (and dispersive). Therefore, as shown in [43][44][45], the value that best mimics the feedback of small scales onto the large scales in a LES can differ depending partially on the numerical methods employed and on the specific problem. In practice, one needs a calibration of the different SGS parameters to maximize the effectiveness of the gradient model.…”

“…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.…”

Enabling real-time multi-messenger astrophysics discoveries with deep learning

“…In the same way that numerical relativity simulations of BBH mergers have been critical for the detection and characterization of these sources with GW observations, numerical relativity simulations of BNS and NSBH mergers are critical to get insights into the physical processes that may lead to the production of electromagnetic and astro-particle counterparts, and to better interpret MMA observations 67 . These modeling efforts do not currently benefit from DL, but recent studies have suggested the possibility to improve the efficiency and robustness of simulations, enabling the inclusion of detailed microphysics [68][69][70][71][72] , and a significance increase in the speed with which partial different equations are solved 73,74 .…”

Comparison of momentum transport models for numerical relativity

“…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.…”