Scale separation for implicit large eddy simulation

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.

Physics of Fluids, 1999

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide a...

Springer Proceedings in Physics, 2009

Turbulence that occurs in nature, or in engineering flows, is usually not, even approximatively, homogeneous. There are frequent variations of the mean velocity with position. By explicating the scale-by-scale energy budget of nonhomogeneous turbulence, it has been argued that the subgrid-scale (SGS) stress tensor should encompass two types of interactions [1, 2]: (i) between the mean velocity and the resolved fluctuating velocities (the rapid part of the SGS stress) and (ii) among the resolved fluctuating velocities themselves (the slow part of the SGS stress). The rapid part is related to the large-scale distortion, while the slow part is associated with the Kolmogorov's energy cascade . Interestingly, these developments end up with a shear-improved Smagorinsky model (SISM) [1], for which the SGS viscosity writes

Physics of Fluids

We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.

Journal of Computational Physics, 2004

Upwind schemes were judged inappropriate for performing accurate large eddy simulations of turbulent flow owing to the artificial dissipation that is present at high wavenumbers of the energy content. Such a conclusion has been drawn also from some results obtained by adopting Finite Difference schemes. The present paper illustrates the performances of some new Finite Volume upwind discretization of the convective terms in the case of the 1-D Burgers model equation while studying the effects of numerical discretization on several Sub-Grid Scales turbulence models, starting from the classical static and dynamic eddy viscosity models through the recent deconvolution-based ones. Basing on previously published papers, large eddy simulations along with a deconvolution-based procedure for de-filtering the evolving variable, have been originally developed and applied. It will be shown how the coherent application of the procedure allows us to develop high-order accurate Finite Volume upwind schemes, which maintain a good spectral resolution in the entire range of resolved scale. Such schemes can be candidate for performing accurate simulations of real turbulence.

Journal of Fluid Mechanics, 1992

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Fame-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 968 grid using Fourier collocation methods. Extensive comparisons between the direct and modelled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence conducted on a coarse 32a gridis shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme’s truncation error and the subgrid-scale model are linked, which raises the question of how accurate the computational results are. The link between the SGS model and truncation error can be beneficially exploited by developing discretization methods for subgrid-scale modeling, or vice versa. Approaches where the SGS model and the numerical discretization scheme are fully merged are called implicit LES (ILES) methods. In order to improve on modeling uncertainties, a systematic framework is proposed for design, analysis, and optimization of nonlinear discretization schemes for implicit LES. The resulting adaptive local deconvolution method (ALDM) for implicit LES is a finite volume method based on a nonlinear deconvolution operator and a numerical flux function. Free parameters inherent to the discretization allow to control the truncation error. They are calibrated in such a way that the truncation error acts as a physically motivated SGS model. An automatic optimization based on an evolutionary algorithm is employed to obtain a set of parameters that results in an optimum match between the spectral numerical viscosity and theoretical predictions of the spectral eddy viscosity for isotropic turbulence. The method is formulated for LES of turbulent flows governed by the incompressible Navier-Stokes equations and for passive-scalar mixing. ALDM has shown the potential for providing a reliable, accurate, and efficient method for LES. Various applications, such as three-dimensional homogeneous isotropic turbulence, transitional and turbulent plane channel flow, and turbulent boundary-layer separation, demonstrate the good performance of the implicit model. Computational results agree well with theory and experimental data and show that the implicit SGS model performs at least as well as established explicit models, for most considered applications the performance is even better. This is possible because physical reasoning is incorporated into the design of the discretization scheme and discretization effects are fully taken into account within the SGS model formulation.

Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motions is so large that the computational cost becomes prohibitive. In large-eddy simulation (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is modeled through a subgrid scale (SGS) model. This process enables a reduction of the computational cost by several orders of magnitude. Given that the accurate representation and prediction of turbulence is needed in many engineering and scientific applications, validation of SGS models must be considered a task of paramount importance. In particular, the analysis must be framed in the context of a convergence study, which is the cornerstone of validation in computational fluid dynamics. In addition, the grid requirements must be determined for LES to be deemed as a cost-saving approach when compared to DNS. Common benchmark solutions for LES are simple hydrodynamic cases such as forced or decaying isotropic turbulence (Métais & Lesieur 1992), spatial or temporal mixing layers (Vreman et al. 1996, 1997) and plane turbulent channel flow (Piomelli et al. 1988; Germano et al. 1991; Chung & McKeon 2010), among others. See Bonnet et al. (1998) for an overview of LES validation. Most SGS models assume that the effective filter cutoff lies within the inertial range, and the Reynolds number and grid resolutions must comply with this requirement in order to faithfully assess the performance of the models. In unbounded flows, like isotropic turbulence, LES can be computed at relatively coarse grid resolutions while still meeting this condition. However, this is not the case in the logarithmic region of wall-bounded flows, where the energy-containing eddies have sizes proportional to the distance to the wall (Jiménez 2012; Larsson et al. 2016). In this case, the LES grid must be accordingly reduced in all directions, increasing the computational cost. This approach is known as wall-resolved LES (WRLES) and can be achieved, for example, through nested grids (Sullivan et al. 1996) such as the one depicted in Figure 1. Actual WRLES are scarce, and typically, only the wall-normal resolution is properly refined according to the size of the energy-containing eddies, while the wall-parallel directions remain under-resolved. The grid requirements become more restrictive in the buffer layer, where the viscous effects are non-negligible. If the near-wall grid resolution does not suffice to capture the energy-containing eddies, most SGS models perform poorly (Jiménez & Moser 2000). The consequence is that the majority of validation studies in turbulent channel flows are WRLES and, hence, their Reynolds numbers tend to be relatively low to make the computational cost affordable (Choi & Moin 2012). However, it is not clear whether the SGS models are active enough at these low Reynolds numbers to adequately measure their performance. In order to test higher Reynolds numbers without the burden of the wall, a possible solution is the implementation of wall models that act as a surrogate of the near-wall dynamics, or the wall-less channel flow proposed by Lozano-Durán &

Physics of Fluids, 2008

Stochastic coherent adaptive large eddy simulation ͑SCALES͒ is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most "energetic" coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier-Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Re = 72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.

Journal of Computational Physics, 2003

Numerical errors in large-eddy simulations (LES) arise from aliasing and discretization errors, and errors in the subfilter-scale (SFS) turbulence model. Using a direct numerical simulation (DNS) dataset of stably stratified shear flow to perform a priori tests, we compare the numerical error from several finite difference schemes to the magnitude of the SFS force. This is an extension of GhosalÕs analysis [J. Comput. Phys. 125 (1996) 187] to realistic flow fields. By evaluating different grid resolutions as well as different filter-grid ratios, we provide guidelines for LES: for a secondorder finite difference scheme, a filter-grid ratio of at least four is desired; for a sixth-order Pad e e scheme, a filter-grid ratio of two is sufficient.