Implicit Subgrid-Scale Modeling for the Large-Eddy Simulation of Compressible Turbulence (original) (raw)
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On discretization errors and subgrid scale model implementations in large eddy simulations
Journal of Computational Physics, 2009
We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier-Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.
Subgrid-scale modeling for large-eddy simulations of compressible turbulence
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.
Implicit Turbulence Modeling by Finite Volume Methods
… Simulation of Turbulent Flows and Noise …, 2009
Turbulence modeling and the numerical discretization of the Navier-Stokes equations are strongly coupled in large-eddy simulations. The truncation error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale model. The subject of this thesis is the analysis and the control of local truncation errors in large-eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method has been developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model accurately representing the effects of unresolved scales. Various applications demonstrate the efficiency and reliability of the new method as well as the superiority of an holistic approach.
… in numerical methods in …, 1994
Second-and fourth-order-accurate spatial discretization methods give rise to discretization errors which are larger than the corresponding subgrid terms in large eddy simulation of compressible shear layers in 2D, if the ratio between the filter width and the grid spacing is close to one. Even if an exact representation for the subgrid-scale contributions is assumed, large eddy simulation is accurate only if this ratio is sufficiently larger than one. In that regime fourth-order methods are more accurate than second-order methods. An analysis of the data obtained from two-dimensional direct numerical simulations of compressible shear layers substantiates these assertions.
Analysis of truncation errors and design of physically optimized discretizations
Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations. Implicit LES can be made rigorous by requiring that the numerical dissipation approximates the SGS dissipation obtained from the analysis of nonlinear interactions in turbulence.
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.
ALDM - A modeling environment for implicit large-eddy simulation
Quality and Reliability of Large-Eddy Simulations, 2008
Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. Relevant discretizations are e.g. finite-volume schemes with a nonlinear regularization to maintain nonlinear stability. Whereas previous approaches in implicit subgrid-scale (SGS) model- ing employed available discretization schemes without analyzing the effective SGS model, and not incorporating physical modeling approaches into the implicit model, we have developed an approach where a full coupling of SGS model and discretization scheme is accomplished. The ALDM (Adaptive Local Deconvolution Method) approach is introduced as an implicit subgrid-scale modeling environment and discussed with respect to its numerical and turbulence-theoretical background. We summarize recent accomplishments in terms of complex flows computed successfully with ALDM and provide a brief outlook on future work.
Implicit Turbulence Modeling for Large-Eddy Simulation
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.
Subgrid-scale modeling and implicit numerical dissipation in DG-based Large-Eddy Simulation
Over the past few years, high-order discontinuous Galerkin (DG) methods for Large-Eddy Simulation (LES) have emerged as a promising approach to solve complex turbulent flows. However, despite the significant research investment, the relation between the discretization scheme, the subgrid-scale (SGS) model and the resulting LES solver remains unclear. This paper aims to shed some light on this matter. To that end, we investigate the role of the Riemann solver, the SGS model, the time resolution, and the accuracy order in the ability to predict a variety of flow regimes, including transition to turbulence, wall-free turbulence, wall-bounded turbulence, and turbulence decay. The transitional flow over the Eppler 387 wing, the Taylor-Green vortex problem and the turbulent channel flow are considered to this end. The focus is placed on post-processing the LES results and providing with a rationale for the performance of the various approaches.