Daniele Carati

On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation

The large-eddy simulation (LES) equations are obtained from the application of two operators to the Navier{Stokes equations: a smooth lter and a discretization operator. The introduction ab initio of the discretization influences the structure of the unknown stress in the LES equations, which now contain a subgrid-scale stress tensor mainly due to discretization, and a filtered-scale stress tensor mainly due to filtering. Theoretical arguments are proposed supporting eddy viscosity models for the subgrid-scale stress tensor. However, no exact result can be derived for this term because the discretization is responsible for a loss of information and because its exact nature is usually unknown. The situation is different for the filtered-scale stress tensor for which an exact expansion in terms of the large-scale velocity and its derivatives is derived for a wide class of filters including the Gaussian, the tophat and all discrete filters. As a consequence of this generalized result, the filtered-scale stress tensor is shown to be invariant under the change of sign of the large-scale velocity. This implies that the filtered-scale stress tensor should lead to reversible dynamics in the limit of zero molecular viscosity when the discretization effects are neglected. Numerical results that illustrate this effect are presented together with a discussion on other approaches leading to reversible dynamics like the scale similarity based models and, surprisingly, the dynamic procedure.

On the representation of backscatter in dynamic localization models

The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time‐step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that th...

On the comparison of turbulence intensities from large-eddy simulation with those from experiment or direct numerical simulation

The relation between the Reynolds stresses from experiment or direct numerical simulation (DNS) and large-eddy simulation (LES) is reviewed. As is well known, the Reynolds stresses can only be reconstructed from a LES when the average contribution from the subgrid-scale model is taken into account. However, in the case of LES using traceless models (e.g., effective viscosity models: Smagorinsky model, dynamic Smagorinsky model, etc.), or even partially traceless models (e.g., mixed models), only the deviatoric Reynolds stresses can be reconstructed. This obvious point is often overlooked in the literature. It has important consequences in all flows with at least one inhomogeneous direction (channels, boundary layers, wakes, shear layers, jets, etc.): as far as the rms turbulence intensities are concerned, one can only properly reconstruct, and thus directly compare with experimental or DNS data, their deviation from isotropy.

Energy transfers in forced MHD turbulence

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.

Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling

The numerical large eddy simulation (LES) technique is tested on decaying magnetohydrodynamic (MHD) turbulence. The LES approach allows for a strong reduction in computational cost compared to direct numerical simulations by modeling the effects of the smallest turbulent scales instead of computing them directly. Two small-scale models of eddy-viscosity type are presented for this purpose in combination with a procedure for the self-consistent calculation of the model parameters in the course of the simulation. The method is successfully tested by comparing the obtained results to a high-resolution direct numerical simulation of decaying three-dimensional MHD turbulence.

Magnetohydrodynamic turbulence at moderate magnetic Reynolds number

We consider the case of homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field at low to moderate magnetic Reynolds numbers (by moderate we mean here values as high as 20). When the magnetic Reynolds number is vanishingly small (

Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence

R_m \ll 1

Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamic turbulence

), it is customary to simplify the governing magnetohydrodynamic (MHD) equations using what is known as the quasi-static (QS) approximation. As the magnetic Reynolds number is increased, a progressive transition between the physics described by the QS approximation and the MHD equations occurs. We show here that this intermediate regime can be described by another approximation which we call the quasi-linear (QL) approximation. For the numerical simulations performed, the predictions of the QL approximation are in good agreement with those of MHD for magnetic Reynolds number up to

Hyper viscosity and vorticity-based models for subgrid-scale modeling

R_m \sim 20

Free Energy Cascade in Gyrokinetic Turbulence

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