Filter size definition in anisotropic subgrid models for large eddy simulation on irregular grids (original) (raw)

A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence

Journal of Fluid Mechanics, 2007

A new subgrid eddy-viscosity model is proposed in this paper. Full details of the derivation of the model are given with the assumption of homogeneous turbulence. The formulation of the model is based on the dynamic equation of the structure function of resolved scale turbulence. By means of the local volume average, the effect of the anisotropy is taken into account in the generalized Kolmogorov equation, which represents the equilibrium energy transfer in the inertial subrange. Since the proposed model is formulated directly from the filtered Navier–Stokes equation, the resulting subgrid eddy viscosity has the feature that it can be adopted in various turbulent flows without any adjustments of model coefficient. The proposed model predicts the major statistical properties of rotating turbulence perfectly at fairly low-turbulence Rossby numbers whereas subgrid models, which do not consider anisotropic effects in turbulence energy transfer, cannot predict this typical anisotropic tu...

An Explicit Filtering Method for Large Eddy Simulation on Unstructured Meshes

40th Fluid Dynamics Conference and Exhibit, 2010

This paper presents the development of an explicit filtering method for Large Eddy simulation in the framework of unstructured grids. The proposed method relies on the approximate deconvolution model, complemented with a modified Smagorinsky term. This term aims at accounting for long-range interactions in the wavenumber space between resolved and subgrid scales. Both a classical and a multiscale formulation of this term are considered. An analytical evaluation procedure is described in order to adjust the model coefficient to our explicit filtering framework. The method relies on the introduction of a discrete filtering operator. For that purpose, a simple volume averaging operator has been chosen in order to perform explicit filtering because of its ease of implementation on unstructured meshes. A discrete characterization procedure of this operator is also proposed in order to estimate locally in space the shape of the filter which is required for the analytical evaluation of the Smagorinsky coefficient. The method is assessed using both hexahedral and tetrahedral grids on a classical homogneneous isotropic turbulence test case. First results obtained for the turbulent flow around a circular cylinder, at a diameter-based Reynolds number of 3,900 are also presented.

Towards exact subgrid-scale models for explicitly filtered large-eddy simulation of wall-bounded flows

The equations for large-eddy simulation (LES) are formally derived by applying a lowpass filter to the Navier-Stokes (NS) equations . Typically, no explicit filter form is specified, and the discrete differentiation operators act as an effective implicit filter. The resulting velocity field is then assumed to be representative of the filtered velocity. However, although the discrete operators have a low-pass filtering effect, the associated filter acts only in the single spatial direction in which the derivative is applied , and thus each term in the NS equations takes on a different filter form. In addition, numerical errors and the frequency content are difficult to control for the implicit filter approach, and the solutions are grid dependent .

A Tensor-Diffusivity Subgrid Model for Large-Eddy Simulation

ERCOFTAC Series, 1999

Subgrid-scale models for large-eddy simulation that are based on exact series expansions for ltered products are considered. In particular, if the rst two terms are retained, the result is a di usive subgrid term with a tensor di usivity. T h i s tensor is proportional to the rate-of-strain tensor of the large-scale velocity eld. This leads to negative di usion in the stretching directions. Implications of this result are considered for the ltered scalar advection-di usion equation and for the momentum equation for incompressible uid ow. When coupled with a dynamic Smagorinsky term to form a mixed model, very encouraging results are shown for turbulent, isotropic decay and for turbulent c hannel ow. In addition, it is shown that the model, mixed or not, transforms appropriately when di ering frames of reference are considered. Modi cations to the model are suggested for the case in which the un ltered eld(s) has discontinuities.

Vector level identity for dynamic subgrid scale modeling in large eddy simulation

Physics of Fluids, 2002

The most commonly used dynamic subgrid scale model is based on the Smagorinsky eddy viscosity model with the model coefficient computed dynamically through the tensor level identity by Germano [et al.] However, the tensor level identity does not explicitly account for the effect of the discretization of the governing equations, and thus the computational results strongly depend on grid resolution, especially in a simulation with poor resolution. In this paper, we propose a new dynamic procedure with the vector level identity, which takes the effect of grid resolution into consideration. The new procedure is tested for the dynamic Smagorinsky eddy viscosity model with the vector level identity. All computational tests were done on turbulent channel flow. The numerical results confirm that the mean velocity profile computed using the new subgrid scale model does not depend on the grid resolution.

A dynamic mixed subgrid-scale model for large eddy simulation on unstructured grids: application to turbulent pipe flows

Journal of Physics: Conference Series, 2014

The paper presents a consistent large eddy simulation (LES) framework which is particularly suited for implicitly filtered LES with unstructured finite volume (FV) codes. From the analysis of the subgrid-scale (SGS) stress tensor arising in this new LES formulation, a novel form of scale-similar SGS model is proposed and combined with a classical eddy viscosity term. The constants in the resulting mixed model are then computed trough a new, cheaper, dynamic procedure based on a consistent redefinition of the Germano identity within the new LES framework. The dynamic mixed model is implemented in a commercial, unstructured, finite volume solver and numerical tests are performed on the turbulent pipe flow at Reτ = 320−1142, showing the flexibility and improvements of the approach over classical modeling strategies. Some limitations of the proposed implementation are also highlighted.

A statistical subgrid scale model for large eddy simulations

2013

Çinlar velocity is a promising subgrid velocity model for large eddy simulation. The energy spectrum plays a central role for modeling the subgrid stress term in filtered Navier-Stokes equations. Considering a truncated Gamma distribution for radius of eddies, the subgrid scale energy spectrum has been computed analytically. In this study, we develop a new subgrid stress model for representing the small scale effects in LES by defining the parameters of the energy spectrum.