A Mathematical Analysis of Scale Similarity

AbstractScale similarity is found in many natural phenomena in the universe, from fluid dynamics to astrophysics. In large eddy simulations of turbulent flows, some sub-grid scale (SGS) models are based on scale similarity. The earliest scale similarity SGS model was developed by Bardina et al., which produced SGS stresses with good correlation to the true stresses. In the present study, we perform a mathematical analysis of scale similarity. The analysis has revealed that the ratio of the resolved stress to the SGS stress isγ2, whereγis the ratio of the second filter width to the first filter width, under the assumption of small filter width. The implications of this analysis are discussed in the context of large eddy simulation.

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Similarities in the Development of Numerical Schemes and Sub-Grid Modeling in Large-Eddy Simulations

Volume 1: Symposia, Parts A, B and C ◽

10.1115/fedsm2009-78326 ◽

2009 ◽

Author(s):

L. E. B. Sampaio ◽

A. O. Nieckele

Keyword(s):

Large Eddy Simulation ◽

Turbulent Flows ◽

Passive Scalar ◽

Large Eddy Simulations ◽

Wave Number ◽

Numerical Schemes ◽

Eddy Simulation ◽

Large Eddy ◽

Mesh Spacing ◽

Discretization Errors

Schemes for the discretization of spatial derivatives commonly employed in the numerical solution of Partial Differential Equations present intrinsic errors that become more important as the wave number content of solution field approaches the Nyquist criteria based on the mesh spacing. In many situations, this can be overcome by simply refining the mesh, so that the wavelength of the structures becomes much larger than the mesh spacing, and the discretization errors become again negligible. However, in some other cases, like in Large-Eddy Simulations of highly turbulent flows, the cost per discretization element is so high that further mesh refinement is prohibitive. In this case, it is more appropriate to work towards understanding and improving the numerical schemes, so that the wider possible range of the spectrum is accurately resolved, and the fewest possible number of degrees of freedom is needed to provide a satisfactory solution. By analyzing the similarities between the problems faced by numerical schemes and the challenges of sub-grid modeling in Large-Eddy Simulations (LES), an alternative for the numerical simulation of turbulence in the context of Large-Eddy Simulation is developed, that accumulates two main functionalities: represent the interaction between unresolved and resolved scales, while keeping the discretization errors at acceptable levels. The proposed scheme is of advective nature and has been applied in several test cases, ranging from simple one-dimensional convection of a passive scalar, to more complex turbulent flows. As a result, a better understanding of the role of discretization errors in Large-Eddy Simulation was obtained.

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Parallel Computing: New Power Aids Understanding of Turbulent Flows

Heat Transfer, Volume 2 ◽

10.1115/imece2002-32818 ◽

2002 ◽

Author(s):

Richard H. Pletcher ◽

Joon S. Lee ◽

Ning Meng ◽

Ravikanth Avancha

Keyword(s):

Turbulent Flows ◽

First Principles ◽

High Performance ◽

Parallel Systems ◽

Large Eddy Simulations ◽

Complex Flows ◽

Complete Understanding ◽

Significant Challenge ◽

Eddy Simulation ◽

Large Eddy

Accurate predictions of turbulent flows occurring in many engineering and environmental applications remain a significant challenge. However, increasing computer power, particularly high performance parallel systems, is enabling more and more complex flows to be solved from first or nearly first principles through direct numerical and large eddy simulation. Such technologies can contribute greatly not only by enabling more accurate predictions but also by revealing details of physics that can contribute to a more complete understanding of turbulence. Several examples where large eddy simulations have provided new details including how rotation and buoyancy alter the structure of turbulence are described.

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Wall-resolved wavelet-based adaptive large-eddy simulation of bluff-body flows with variable thresholding

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.708 ◽

2016 ◽

Vol 788 ◽

pp. 303-336 ◽

Cited By ~ 16

Author(s):

Giuliano De Stefano ◽

Alireza Nejadmalayeri ◽

Oleg V. Vasilyev

Keyword(s):

Turbulent Flows ◽

Bluff Body ◽

Large Eddy Simulations ◽

Eddy Simulation ◽

Computational Mesh ◽

Large Eddy ◽

High Reynolds ◽

The One ◽

Solid Obstacles ◽

Bluff Body Flows

The wavelet-based eddy-capturing approach with variable thresholding is extended to bluff-body flows, where the obstacle geometry is enforced through Brinkman volume penalization. The use of a spatio-temporally varying threshold allows one to perform adaptive large-eddy simulations with the prescribed fidelity on a near optimal computational mesh. The space–time evolution of the threshold variable is achieved by solving a transport equation based on the Lagrangian path-line diffusive averaging methodology. The coupled wavelet-collocation/volume-penalization approach with variable thresholding is illustrated for a turbulent incompressible flow around an isolated stationary prism with square cross-section. Wavelet-based adaptive large-eddy simulations supplied with the one-equation localized dynamic kinetic energy-based model are successfully performed at moderately high Reynolds number. The present study demonstrates that the proposed variable thresholding methodology for wavelet-based modelling of turbulent flows around solid obstacles is feasible, accurate and efficient.

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Simulating flow separation from continuous surfaces: routes to overcoming the Reynolds number barrier

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0002 ◽

2009 ◽

Vol 367 (1899) ◽

pp. 2885-2903 ◽

Cited By ~ 18

Author(s):

Michael Leschziner ◽

Ning Li ◽

Fabrizio Tessicini

Keyword(s):

Reynolds Number ◽

Turbulent Flows ◽

Major Elements ◽

Wall Layer ◽

Navier Stokes ◽

Eddy Simulation ◽

Large Eddy ◽

Rans Models ◽

High Reynolds ◽

Near Wall

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

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