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

This is the final version. Available from AIP Publishing via the DOI in this recordCompressible 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 (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale 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 [W. K. Yeo (CUP, 1993)] 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 -Alfvénic 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 Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.University of GöttingenDeutsche Forschungsgemeinschaft (DFG)Max Planck Institute for Dynamics and Self-OrganizationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y TecnológicoNorth-German Supercomputing Allianc

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

This is the final version. Available from AIP Publishing via the DOI in this recordEven though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics. We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number Ms=0.2-20 as reference data for the most extensive a priori tests performed so far in literature. In these tests, we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicity flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and the direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value > 0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.University of GöttingenDeutsche Forschungsgemeinschaft (DFG)Max Planck Institute for Dynamics and Self-OrganizationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y Tecnológic

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

This is the final version. Available from the American Physical Society via the DOI in this recordLarge-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) models, and one recently proposed nonlinear (NL) SGS model in the realm of compressible magnetohydrodynamic (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 the 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.University of GottingenMax-Planck-Institut MPI für Dynamik und SelbstorganisationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y TecnológicoCentro de Astrofísica y Tecnologías Afines CAT

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

This is the final version. Available on open access from IOP Publishing via the DOI in this recordTurbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment - magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures - models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure () and sonic Mach numbers (). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and closures. We find only mediocre performance of the kinetic eddy-viscosity and closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.University of GottingenDeutsche Forschungsgemeinschaft (DFG)Australian Research Council (ARC

Suppression of lithium depletion in young low-mass stars from fast rotation

This is the final version. Available from EDP Sciences via the DOI in this recordWe compute rotating 1D stellar evolution models that include a modified temperature gradient in convection zones and criterion for convective instability inspired by rotating 3D hydrodynamical simulations performed with the music code. In those 3D simulations wefound that convective properties strongly depend on the Solberg-Høiland criterion for stability. We therefore incorporated this into 1D stellar evolution models by replacing the usual Schwarzschild criterion for stability and also modifying the temperature gradient in convection zones. We computed a grid of 1D models between 0.55 and 1.2 stellar masses from the pre-main sequence to the end of main sequence in order to study the problem of lithium depletion in low-mass main sequence stars. This is an ideal test case because many of those stars are born as fast rotators and the rate of lithium depletion is very sensitive to the changes in the stellar structure. Additionally, observations show a correlation between slow rotation and lithium depletion, contrary to expectations from standard models of rotationally driven mixing. By suppressing convection, and therefore decreasing the temperature at the base of the convective envelope, lithium burning is strongly quenched in our rapidly rotating models to an extent sufficient to account for the lithium spread observed in young open clusters.European Research Council (ERC)Science and Technology Facilities Council (STFC

Effects of stratification on overshooting and waves atop the convective core of M⊙ main-sequence stars

This is the final version. Available from Oxford University Press via the DOI in this record. DATA AVAILABILITY: Data backing this study will be shared on reasonable request to the corresponding author.As a massive star evolves along the main sequence, its core contracts, leaving behind a stable stratification in helium. We simulate two-dimensional convection in the core at three different stages of evolution of a [Formula presented] star, with three different stratifications in helium atop the core. We study the propagation of internal gravity waves in the stably stratified envelope, along with the overshooting length of convective plumes above the convective boundary. We find that the stratification in helium in evolved stars hinders radial motions and effectively shields the radiative envelope against plume penetration. This prevents convective overshooting from being an efficient mixing process in the radiative envelope. In addition, internal gravity waves are less excited in evolved models compared to the zero-age-main-sequence model, and are also more damped in the stratified region above the core. As a result, the wave power is several orders of magnitude lower in mid- and terminal-main-sequence models compared to zero-age-main-sequence stars.European Research CouncilScience and Technology Facilities CouncilUnited States Department of Energ

A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations

This is the final version. Available from Oxford University Press via the DOI in this record. We perform two-dimensional (2D) numerical simulations of core convection for zero-age main-sequence stars covering a mass range from 3 to 20 M. The simulations are performed with the fully compressible time-implicit code MUSIC. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 M models. The simulations cover hundreds to thousands of convective turnover time-scales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance (dov) scales with the stellar luminosity (L) and the convective core radius (rconv). We derive a scaling law dov ∝ L1/3r1/2 conv, which isimplemented in a one-dimensionalstellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses 10 M. Our 2D simulations show the formation of a nearly adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent three-dimensionalsimulations of convection. The most luminous modelsshow a growth in size with time of the nearly adiabatic layer. This growth seemsto slow down asthe upper edge of the nearly adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive time-scale in the overshooting layer.Science and Technology Facilities CouncilEuropean Commissio

Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes

This is the final version. Available from EDP Sciences via the DOI in this recordOur ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH, MUSIC, PPMSTAR, PROMPI, and SLH, which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within ≲3σ of the mean of all simulations on a given grid (1283 and 2563 grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 5123 reference run. The 1283 and 2563 simulations agree within 9% and 4%, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.Science and Technology Facilities Council (STFC)European Research Council (ERC

Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model

This is the final version. Available on open access from Oxford University Press via the DOI in this record. Data availability: The data underlying this article will be shared on reasonable request to the corresponding author.Stellar convection is a non-local process responsible for the transport of heat and chemical species. It can lead to enhanced mixing through convective overshooting and excitation of internal gravity waves (IGWs) at convective boundaries. The relationship between these processes is still not well understood and requires global hydrodynamic simulations to capture the important large-scale dynamics. The steep stratification in stellar interiors suggests that the radial extent of such simulations can affect the convection dynamics, the IGWs in the stably stratified radiative zone, and the depth of the overshooting layer. We investigate these effects using 2D global simulations performed with the fully compressible stellar hydrodynamics code MUSIC. We compare eight different radial truncations of the same solar-like stellar model evolved over approximately 400 convective turnover times. We find that the location of the inner boundary has an insignificant effect on the convection dynamics, the convective overshooting, and the travelling IGWs. We relate this to the background conditions at the lower convective boundary which are unaffected by the truncation, as long as a significantly deep radiative layer is included in the simulation domain. However, we find that extending the outer boundary by only a few per cent of the stellar radius significantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The effect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratification and the given luminosity.European Research Council (ERC)Science and Technology Facilities Council (STFC