A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties

Abstract

Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LES), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale (SGS) dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator 1 and require no assumptions about the nature of the flow or magnetic field. Thus the scope of their applicability ranges from the sub-to the hyper-sonic and -Alfvenic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular the anisotropy, of the flow. Their properties are a priori validated in an accompanying article 2 against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.

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

“…In order to account for cross-helicity effects such as changing cascade dynamics both structural models are expected to be applicable as presented. While the nonlinear model makes no assumptions on the nature of the flow [13], the scalesimilarity model implicitly accounts for changing dynamics [44]. The functional eddy-viscosity model misses this feature.…”

“…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. We employ the primary compressible extension resulting in the following model:…”

“…Formally, this is equivalent to applying a low-pass filter to the ideal compressible MHD equations resulting in expressions of the form [13] ∂ρ ∂t + ∇ · (ρ u) = 0, (1)…”

Intermittent fragmentation and statistical variations during gas collapse in magnetized atomic cooling haloes

“…To include the effect of unresolved, i.e., below the grid-scale, turbulence we employ the nonlinear SGS model for MHD turbulence presented by Vlaykov et al (2016); Grete et al (2016). The main features of this model are that it specifi-cally takes compressibility effects into account and allows for energy transfer in both directions.…”

“…The majority of MHD SGS models have been derived from their incompressible hydrodynamic counterparts, and only few have been tested in the compressible MHD regime (Miki & Menon 2008;Chernyshov et al 2014;Grete et al 2015). Vlaykov et al (2016) and Grete et al (2016Grete et al ( , 2017 have developed an SGS model that explicitly takes into account compressibility effects in MHD turbulence and demonstrated its applicability from the subsonic to the highly supersonic regime. Therefore, it is most suitable for the dynamics of a Direct Collapse scenario.…”