The effect of subgrid-scale models on grid-scale/subgrid-scale energy transfers in large-eddy simulation of incompressible magnetohydrodynamic turbulence

Kessar, Mouloud; Balarac, Guillaume; Plunian, Franck

doi:10.1063/1.4964782

Cited by 12 publications

(25 citation statements)

References 28 publications

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“…Notice however that this is only a part of the non-linear dynamics involved in MHD turbulence. The overall great performance of the gradient model are well known [28,32,33,[49][50][51][52], due to the strong mathematical basis on which it relies. Let us stress that we have explored different initial conditions, finding mainly the same results.…”

Section: B Resultsmentioning

confidence: 99%

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

2020

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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.

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Section: B Resultsmentioning

confidence: 99%

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

2020

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“…The overall performance of the gradient model in the apriori tests, as shown so far, are well known 21, [36][37][38]40,41 . Besides confirming those results for our compressible ideal MHD problem, we here show how the SFS tensorsτ hel and τ adv can also be fit very well by the corresponding gradient models, with the values of P and C best in line with the other tensors.…”

Section: B Performance Of the New Gradient Termsmentioning

confidence: 99%

“…Very detailed works about LES with SGS models have been performed in the context of either incompressible 19,[34][35][36] or compressible 21,25,37-40 MHD, but not, to our knowledge, including an ideal gas equation of state. While the momentum and induction equations have been explored in many different works, the energy evolution has usually been neglected, or only partially considered, since they impose either incompressibility or a polytropic/isothermal equation of state 41 .…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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“…For modeling the SGS terms in Equations (11) to (14), we only care about τ kin describing turbulent motion, τ mag describing the contribution of the turbulent magnetic field to the motion, τ ind describing the turbulent amplification of the magnetic field, and τ enth describing the effect of turbulence on the energy transfer. We neglect the terms (p − p) and Σ pres .…”

Section: Filtered Mhd Equationsmentioning

confidence: 99%

Artificial neural network subgrid models of 2D compressible magnetohydrodynamic turbulence

Rosofsky

Huerta

2020

Phys. Rev. D

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We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to systematically quantify the performance of neural network models to reproduce the physics of these complex simulations. We compare the performance of our neural networks with gradient models, which are extensively used in the extensively in the magnetohydrodynamic literature. Our findings indicate that neural networks significantly outperform gradient models at reproducing the effects of magnetohydrodynamics turbulence. To the best of our knowledge, this is the first exploratory study on the use of deep learning to learn and reproduce the physics of magnetohydrodynamics turbulence.

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The effect of subgrid-scale models on grid-scale/subgrid-scale energy transfers in large-eddy simulation of incompressible magnetohydrodynamic turbulence

Cited by 12 publications

References 28 publications

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

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

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

Artificial neural network subgrid models of 2D compressible magnetohydrodynamic turbulence

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