Implicit Turbulence Modeling by Finite Volume Methods

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, 2011

With implicit large-eddy simulation (ILES) the truncation error of the discretization scheme acts as subgrid-scale (SGS) model for the computation of turbulent flows. Although ILES is comparably simple, numerical robust and easy to implement, a considerable challenge is the design of numerical discretization schemes resulting in a physically consistent SGS model. In this work, we consider the implicit SGS model of the adaptive central-upwind weighted-essentiallynon-oscillatory scheme (WENO-CU6) (Hu, XY, Wang, Q. & Adams, NA, J. Comput. Phys., 229 (2010) 8952-8965.) by incorporating a physically-motivated scale-separation formulation. Scale separation is accomplished by a simple modification of the WENO weights. The resulting modified scheme maintains the shock-capturing capabilities of the original WENO-CU6 scheme while it is also able to reproduce the Kolmogorov range of the kinetic-energy spectrum for turbulence at the limit of infinite Reynolds number independently of grid resolution. For quasi-isentropic compressible turbulence the the pseudo-sound regime of the dilatational kinetic-energy spectrum and the non-Gaussian probabilitydensity function of the longitudinal velocity derivative are reproduced.

Journal of Computational Physics, 1996

net effect of the large number of subgrid eddies is represented by a subgrid force, which is specified in a more or

Journal of Computational Physics, 2011

We assess the performances of three different subgrid scale models in large eddy simulations (LES) of turbulent channel flows. Two regimes are considered: hydrodynamic and magnetohydrodynamic (i.e. in the presence of a uniform wall-normal magnetic field). The simulations are performed using a second-order finite volume (FV) and a pseudo-spectral (PS) method. The LES results are compared with under-resolved results (obtained without model) and direct numerical simulations (DNS). We show that discretization errors affect the FV results in two ways: (1) the flow statistics differ from the spectral estimates in the absence of subgrid model; and (2) the eddy viscosity systematically underestimates the spectral value in the presence of a subgrid model. This is mainly because numerical errors affect the computation of the derivatives, and in particular, they lower the discrete strain rate appearing in the viscous term and the subgrid model. The magnitude of the numerical errors further varies with the mesh resolution and the intensity of the turbulent fluctuations. In this manuscript, a novel formulation of the discrete strain, which was proven successful in homogeneous isotropic turbulence, is used to compute the FV eddy viscosities. Although the average norm of the discrete strain is largely increased using this formulation, the effect on the flow dynamics is marginal. This is explained by analysing the contribution of each term of the discrete kinetic energy balance. It is shown how the underestimation of the discrete viscous dissipation inhibits the effect of the improved discrete strain.

Physics of Fluids, 2002

We present two phenomenological subgrid-scale ͑SGS͒ models for large-eddy simulations ͑LES͒ of compressible turbulent flows. A nonlinear model and a stretched-vortex model are tested in LES of compressible decaying isotropic turbulence. Results of LES at 32 3 , 48 3 , and 64 3 resolution are compared to corresponding 256 3 direct numerical simulations ͑DNS͒ at a turbulent Mach number, M t ϳ0.4. We use numerical schemes based on compact finite differences and study the effects of their order of accuracy on LES results. Both models give satisfactory agreement with DNS for the decay of the total turbulent kinetic energy. The probability densities ͑pdf͒ of energy transfer to subgrid scales obtained from filtered DNS and the SGS models are compared. Both models produce a narrower distribution of energy transfer than corresponding filtered DNS data, with less backscatter. The pdf of the alignment of components of the subgrid stress tensor and the eigenvectors of the rate-of-strain tensor obtained from the models reproduces some features of the DNS results. The pdfs of both energy transfer and relative eigenvector alignment are obtained from DNS and LES after about one large-eddy turnover time from the same initial condition. All tests of the present LES models are therefore a posteriori and none is a priori.

Physics of Fluids, 2007

Approaches to large eddy simulation where subgrid-scale model and numerical discretization are fully merged are called implicit large eddy simulation (ILES). Recently, we have proposed a systematic framework for development, analysis, and optimization of nonlinear discretization schemes for ILES [ Hickel et al., J. Comput. Phys. 213, 413(2006) ]. The resulting adaptive local deconvolution method (ALDM) provides a truncation error which acts as a subgrid-scale model consistent with asymptotic turbulence theory. In the present paper ALDM is applied to incompressible, turbulent channel flow to analyze the implicit model for wall-bounded turbulence. Computational results are presented for Reynolds numbers, based on friction velocity and channel half-width, of Reτ = 180, Reτ = 395, Reτ = 590, and Reτ = 950. All simulations compare well with direct numerical simulation data and yield better results than the dynamic Smagorinsky model at the same resolution. The results demonstrate that the implicit model ALDM provides an accurate prediction for wall-bounded turbulence although model parameters have been calibrated for the infinite Reynolds number limit of isotropic turbulence. The near-wall accuracy can be further improved by a simple modification which is described in the paper.

Computers & Fluids, 2010

The purpose of this paper is to investigate and validate an alternative subgrid model to be used in largeeddy simulations, based on an advective formulation. Rather than modeling the subgrid tensor that appears in the LES formulation as is commonly done, the subgrid force vector, which is the divergence of the subgrid tensor, is modeled directly. It is designed to comply with two basic principles. First, it is required to act only on the smallest scales that the mesh can represent. Second, it must be of an advective nature, which means it must have a preferred direction aligned with the fluid velocity. The results for two benchmark test cases, including Homogeneous Isotropic Turbulence and Turbulent Channel Flow, show that this approach can successfully represent the effect of the small scales on the resolved ones, while guaranteeing numerical stability and greater robustness in adverse mesh environments, when compared to some traditional eddy-viscosity based models, such as the Smagorinsky and the dynamic model from Germano.

Theoretical and Computational Fluid …, 2008

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the sub- grid-scalemodel are linked. One can exploit this link by developing discretizationmethods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGSmodel. The resulting so-called adaptive local deconvolutionmethod (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper,ALDMis evaluated for the separated flowthrough a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2, 808 and Re = 10, 595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered phys- ically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.

Journal of Computational Physics, 2004

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation (LES) is evaluated through the static and dynamic analyses. For the static error analysis, the power spectra of the finite-differencing and aliasing errors are evaluated in the discrete Fourier space, and for the dynamic error analysis LES of isotropic turbulence is performed with various dissipative and non-dissipative schemes. Results from the static analysis give a misleading conclusion that both the aliasing and finite-differencing errors increase as the numerical dissipation increases. The dynamic analysis, however, shows that the aliasing error decreases as the dissipation increases and the finite-differencing error overweighs the aliasing error. It is also shown that there exists an optimal upwind scheme of minimizing the total discretization error because the dissipative schemes decrease the aliasing error but increase the finite-differencing error. In addition, a classical issue on the treatment of nonlinear term in the Navier-Stokes equation is revisited to show that the skew-symmetric form minimizes both the finite-differencing and aliasing errors. The findings from the dynamic analysis are confirmed by the physical space simulations of turbulent channel flow at Re ¼ 23000 and flow over a circular cylinder at Re ¼ 3900.

IOP Conference Series: Materials Science and Engineering, 2010

In this contribution we present the application of a numerical method based on a mesh free interpolation technique (Moving Least-Squares (MLS)) in a finite volume framework to the computation of turbulent flows. Our approach is based on the monotonically implicit Large Eddy Simulation (MILES). The main idea of MILES methodology is the absence of any explicit subgrid scale (SGS) model in the numerical algorithm to solve turbulent flows. As MLS approximations are used to compute the gradients and higher-order derivatives, the parameters of the kernel function plays a crucial role on the properties of the numerical scheme, particularly on the dispersion and dissipation of the method. This allows us to define an implicit filter that acts as a SGS model in turbulence computations. We present the results for the decay of compressible isotropic turbulence, which are very promising, and the our first results computing turbulence flows in presence of walls.