A study of built-in filter for some eddy viscosity models in large-eddy simulation (original) (raw)
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Sharp cutoff versus smooth filtering in large eddy simulation
Physics of fluids, 2002
The large eddy simulation ͑LES͒ equations of turbulent flows are formally derived by applying a low-pass filter to the Navier-Stokes equations. As a result the subgrid-scale ͑SGS͒ stress tensor strongly depends on the assumed filter shape, which causes a SGS model to be filter dependent. In particular, depending on the choice of the filter the corresponding SGS model should satisfy very different requirements in terms of large scale dynamics and kinetic energy budget. This paper is an attempt to systematically study the effect of the filter shape on the subgrid scale model and its subsequent effect on LES. For the sake of simplicity, we consider numerical simulation of a one-dimensional homogeneous flow, governed by the viscous Burgers equation. Large eddy simulations of the solution of the Burgers problem are performed using subgrid scale models obtained by filtering data from direct numerical simulations. Diagnostics include temporal evolution of energy and dissipation as well as energy spectra. It is demonstrated both theoretically and numerically that the assumed filter shape can have a significant effect on LES in terms of spectral content and physical interpretation of the solution. The results are generalized for LES of three-dimensional turbulent flows and specific recommendations for the use of filters and corresponding SGS models are made.
A Study on the Filtering Approach and Turbulence Modeling for LES
International Journal of Computer Applications, 2014
During the past decades, Large-Eddy Simulation (LES) has been demonstrated to be a useful research tool for understanding the physics of turbulence as well as an accurate and sophisticated predictive method for flows of engineering interest. The LES is numerical technique and is based on the separation between large and small scales in which the largescale motion is exactly calculated and the effects of small sales or so called sub grid-scale motions are modelled. It is also important to note that the explicit or implicit filter representations like spectral cutoffs or numerical discretizations are commonly used in LES of turbulent flows. Strictly we can say that in LES we need to filter the Navier-Stokes equations in turbulence. Therefore, the study on the filtering approach in turbulence is the main objects of the present research, and in this study we have elaborately studied on this filtering approach and analyzed some general algebraic properties of the filtered representations. It is shown that the averaged equations are the same in terms of the generalized central moments, and then we have defined the resolved turbulence using these average properties. The algebraic consistency rules related with the resolved quantities to the turbulent stresses are derived and their possible use in sub grid-scale modelling is examined. In this study, we have also discussed about the standard Smagorinsky model for LES and then we derived an expression to determine the Smagorinsky constant dynamically, which suppose to be assured the consistency between the filter and the sub grid-scale model. Finally, we have derived the governing equations for LES by applying the filtering approach to the Navier-Stokes equations.
Determination of subfilter energy in large-eddy simulations
Journal of Turbulence, 2004
A methodology is presented for the determination of the subfilter energy in large-eddy simulations (LES). The model assumes universal-equilibrium turbulence in the subgrid scales and is based on the integration of semi-empirical functions for energy spectra of homogeneous isotropic turbulence. The model depends on the Reynolds number, the integral length scale and its ratio to the flow containment, as well as the LES resolution. On the one hand, the formalism is suitable for an a priori estimation of the subgrid-energy level, which is useful for preparatory LES set-up. Charts are drawn which connect the Reynolds number and the LES resolution to the expected level of subgrid energy. Furthermore, the difference is evaluated between the present model and a model based on the integration of an idealized k −5/3 spectrum, which is related to the high-Reynoldsnumber asymptotic behaviour of the energy spectrum. On the other hand, the presented methodology can be used as a model for the subgrid energy in an actual LES, as part of a subgrid-scale stress model. The formulation of the model, based on equations which directly use resolved-scale LES properties, is briefly outlined.
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.
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 .
2007
A turbulent subfilter viscosity for large eddy simulation (LES) models is proposed, based on Heisenberg's mechanism of energy transfer. Such viscosity is described in terms of a cutoff wave number, leading to relationships for the grid mesh spacing, for a convective boundary layer (CBL). The limiting wave number represents a sharp filter separating large and small scales of a turbulent flow and, henceforth, Heisenberg's model agrees with the physical foundation of LES models. The comparison between Heisenberg's turbulent viscosity and the classical ones, based on Smagorinsky's parameterization, shows that both procedures lead to similar subgrid exchange coefficients. With this result, the turbulence resolution length scale and the vertical mesh spacing are expressed only in terms of the longitudinal mesh spacing. Through the employment of spectral observational data in the CBL, the mesh spacings, the filter width and the subfilter eddy viscosity are described in terms of the CBL height. The present development shows that Heisenberg's theory naturally establishes a physical criterium that connects the subgrid terms to the large-scale dimensions of the system. The proposed constrain is tested employing a LES code and the results show that it leads to a good representation of the boundary layer variables, without an excessive refinement of the grid mesh. r
A higher-order subfilter-scale model for large eddy simulation
Journal of Computational and Applied Mathematics, 2003
This paper presents a new sublter-scale stress model for large eddy simulation. The unknown velocity eld is represented in terms of the ltered velocity by using a higher-order Pad e approximation of the Fourier transform of the Gaussian lter. This accurate approximation of the velocity eld yields an improved sublter-scale stress tensor accounting for the information lost in the ltering process. The accuracy of the sublter-scale stress tensor is especially important in the large eddy simulation of complex ows, such as geophysical ows, where the practical grid size is much larger than the scale of turbulent motion. We illustrate our approach through two simple one-dimensional numerical examples. We also present a rigorous mathematical analysis for this new large eddy simulation model.
New Trends in Large-Eddy Simulations of Turbulence
Annual Review of Fluid Mechanics, 1996
The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky's model. We show how Kraichnan's spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scalesimilarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices.
Mixed modeling for large-eddy simulation: the minimum-dissipation-bardina model
2018
The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES) approach. The current work applies a volume filtering procedure according to Schumann (1975). To demonstrate the procedure the Schumann filter is first applied to a convection-diffusion equation. The Schumann filter results in volume-averaged equations, which are not closed. To close these equations a model is introduced, which represents the interaction between the resolved scales and the small subgrid scales. Here, the anisotropic minimum-dissipation model of Rozema et al. (2015) is considered. The interpolation scheme necessary to evaluate the convective flux at the cell faces can be viewed as a second filter. Thus, the convection term of the filtered convection-diffusion equation can be interpreted as a double-filtered term. This term is approxima...