Abstract
In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid-scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid-scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamic procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid-scale turbulence energy model allows for a particularly elegant and physically well-motivated way of preserving momentum and energy conservation in adaptive mesh refinement (AMR) simulations. Moreover, the notion of shear-improved models for in-homogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.
Highlights
Turbulent flows with high Reynolds numbers are often encountered in computational astrophysics
These results demonstrate how scale-invariant quantities computed with the shear-improved SGS model can be utilized to investigate statistical properties of turbulence
It is a particular difficulty of validating large eddy simulation (LES) in astrophysics that neither direct numerical simulation (DNS) nor sufficiently accurate experimental data exist
Summary
Turbulent flows with high Reynolds numbers are often encountered in computational astrophysics. In simulations of statistically stationary isotropic turbulence, the inertial subrange is very narrow for computationally feasible resolutions because the bottleneck effect distorts the spectrum over a large range of high wave numbers below the Nyquist wavenumber (Falkovich, 1994; Dobler et al, 2003; Schmidt et al, 2006a) It appears that LES with an explicit SGS model, such as the K-equation model, can reduce the bottleneck effect to some degree and reproduce scalings from ILES or DNS at lower resolution (Haugen and Brandenburg, 2006; Woodward et al, 2006; Schmidt, 2010). Inhomogeneous and non-stationary turbulence can be treated by dynamical procedures for the calculation of closure coefficients or shear-improved SGS models, which decompose the numerically resolved flow into mean and fluctuating components
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