A nonlinear structural subgrid-scale closure for compressible MHD. II. <i>A priori</i> comparison on turbulence simulation data

Grete, Philipp; Vlaykov, Dimitar; Schmidt, Wolfgang; Schleicher, Dominik R. G.

doi:10.1063/1.4954304

Cited by 26 publications

(30 citation statements)

References 47 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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“…In the absence of detailed 3D spatio-temporal observations and/or experimental data, numerical simulations are often used to support the interpretation of observations or, in the case of turbulence research, have become one of the major drivers of scientific advances. This pertains, for example, to studying energy dissipation and turbulent energy cascades, (e.g., Yang et al 2016;Grete et al 2017;Andrs et al 2018) or to turbulence modeling (Clark et al 1979;Germano et al 1991;Chernyshov et al 2012;Grete et al 2016).…”

Section: Introductionmentioning

confidence: 99%

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

Grete

O’Shea

Beckwith

2020

ApJ

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Turbulence simulations play a key role in advancing the general understanding of the physical properties turbulence and in interpreting astrophysical observations of turbulent plasmas. For the sake of simplicity, however, turbulence simulations are often conducted in the isothermal limit. Given that the majority of astrophysical systems are not governed by isothermal dynamics, we aim to quantify the impact of thermodynamics on the physics of turbulence, through varying adiabatic index, γ, combined with a range of optically thin cooling functions. In this paper, we present a suite of ideal magnetohydrodynamics simulations of thermally balanced stationary turbulence in the subsonic, super-Alfvénic, high β p (ratio of thermal to magnetic pressure) regime, where turbulent dissipation is balanced by two idealized cooling functions (approximating linear cooling and free-free emission) and examine the impact of the equation of state by considering cases that correspond to isothermal, monatomic and diatomic gases. We find a strong anticorrelation between thermal and magnetic pressure independent of thermodynamics, whereas the strong anticorrelation between density and magnetic field found in the isothermal case weakens with increasing γ. Similarly, with the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing γ. This suggests that there exists a degeneracy in these relations with respect to thermodynamics and Mach number in this regime, which is dominated by slow magnetosonic modes. These results have implications for attempts to infer (e.g.) Mach numbers from (e.g.) Faraday rotation measurements, without additional information regarding the thermodynamics of the plasma. However, our results suggest that this degeneracy can be broken by utilizing higher-order moments of observable distribution functions.

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“…In our a priori analysis [24] we tested three different model families, eddy-dissipation, scale-similarity, and nonlinear models, with different normalizations. All models were tested against the expressions (5) and (6) where the filtered nonlinear term is not split into additional components.…”

Section: Methodsmentioning

confidence: 99%

“…The model allows for energy transfer down-and up-scale and, as a structural closure, aims at reproducing closely the properties of the SGS terms and not just their effects on the large scales. c. The nonlinear (NL) model is another structural model and exhibited the highest correlations with reference data in a priori tests [23,24]. It can be derived from Taylor expansion of the inverse filter kernel [13,28] and requires no further assumptions about the underlying flow features.…”

Section: Methodsmentioning

confidence: 99%

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Comparative statistics of selected subgrid-scale models in large-eddy simulations of decaying, supersonic magnetohydrodynamic turbulence

et al. 2017

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Large eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by direct simulations due to their complexity, for example, in the highly turbulent regime. However, their accuracy and success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in the simulation. We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and the scale-similarity (SS) model, and one recently proposed nonlinear (NL) SGS model in the realm of compressible MHD turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number Ms ≈ 3) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model and filter, we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore, we compare the temporal evolution of lower and higher order statistical moments of the spatial distributions of kinetic and magnetic energy, vorticity, current density, and dilatation magnitudes. We find no statistical influence on the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. In addition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both EV and NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipation on the smallest scales. We demonstrate that the nonlinear model improves higher order statistics already with a small explicit filter, i.e. a three-point stencil. The results of e.g. the structure functions or the skewness and kurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution. In addition, no additional regularization to stabilize the model is required. We conclude that the nonlinear model with a small explicit filter is suitable for application in more complex scenarios when higher order statistics are important.

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A nonlinear structural subgrid-scale closure for compressible MHD. II. A priori comparison on turbulence simulation data

Cited by 26 publications

References 47 publications

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

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

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

Comparative statistics of selected subgrid-scale models in large-eddy simulations of decaying, supersonic magnetohydrodynamic turbulence

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