Analytical and numerical study of resolution criteria in large-eddy simulation

The present work investigates the influence of the primary filter resolution on various turbulence statistics and the representation of vortical structures in Large-Eddy Simulation (LES) of homogeneous isotropic turbulent flow. The resolution effects are investigated both analytically and numerically for an ideal LES solution with negligible modeling and numerical errors, and as such equivalent to filtered direct numerical simulation data. The Taylor-Green vortex is considered for the numerical investigation. Several resolution criteria, found in the literature, which prescribe the filter width requirements for LES, are investigated and their effect on various turbulent statistics is evaluated analytically. Further, the resolution effect on vortical structures is evaluated numerically using the Taylor-Green vortex. Finally, an optimal resolution for LES is derived via a multi-objective optimization, maximizing the resolved fractions of specifically chosen turbulent quantities while minimizing the computat...

[1]  Energy spectrum in the dissipation range of fluid turbulence , 1996 .

[2]  Dominique Laurence,et al.  Optimal Unstructured Meshing for Large Eddy Simulations , 2008 .

[3]  Victor Yakhot,et al.  THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ANOMALOUS SCALING OF STRUCTURE FUNCTIONS AND DYNAMIC CONSTRAINTS ON TURBULENCE SIMULATIONS , 2007 .

[4]  Y. Tsuji.  Intermittency effect on energy spectrum in high-Reynolds number turbulence , 2004 .

[5]  Z. She,et al.  On the universal form of energy spectra in fully developed turbulence , 1993 .

[6]  D. Carati,et al.  A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence , 2007 .

[7]  K. Sreenivasan.  On the universality of the Kolmogorov constant , 1995 .

[8]  Steven A. Orszag,et al.  On the Elimination of Aliasing in Finite-Difference Schemes by Filtering High-Wavenumber Components , 1971 .

[9]  T. Kármán,et al.  On the Statistical Theory of Isotropic Turbulence , 1938 .

[10]  Z. Warhaft,et al.  On the onset of high-Reynolds-number grid-generated wind tunnel turbulence , 1996, Journal of Fluid Mechanics.

[11]  Diego Donzis,et al.  The bottleneck effect and the Kolmogorov constant in isotropic turbulence , 2010, Journal of Fluid Mechanics.

[12]  Yukio Kaneda,et al.  High-resolution direct numerical simulation of turbulence , 2006 .

[13]  L. Davidson.  Large Eddy Simulations: How to evaluate resolution , 2009 .

[14]  William K. George,et al.  Reynolds Number Dependence of Energy Spectra in the Overlap Region of Isotropic Turbulence , 2000 .

[15]  C. Doering,et al.  Links between dissipation, intermittency, and helicity in the GOY model revisited , 2005, nlin/0510038.

[16]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[17]  Y. Kaneda,et al.  Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics , 2007, Journal of Fluid Mechanics.

[18]  On the use of high‐order finite‐difference discretization for LES with double decomposition of the subgrid‐scale stresses , 2008 .

[19]  R. Moser,et al.  Optimal LES formulations for isotropic turbulence , 1999, Journal of Fluid Mechanics.

[20]  S. Pope.  Turbulent Flows: FUNDAMENTALS , 2000 .

[21]  Ismail Celik,et al.  Index of resolution quality for large eddy simulations , 2005 .

[22]  Diego Donzis,et al.  Dissipation and enstrophy in isotropic turbulence: Resolution effects and scaling in direct numerical simulations , 2008 .

[23]  R. Moser,et al.  Optimal large-eddy simulation results for isotropic turbulence , 2004, Journal of Fluid Mechanics.

[24]  G. Taylor,et al.  Mechanism of the production of small eddies from large ones , 1937 .

[25]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[26]  Steven A. Orszag,et al.  Numerical Simulation of the Taylor-Green Vortex , 1973, Computing Methods in Applied Sciences and Engineering.

[27]  Kemal Hanjalic,et al.  Vortical structures and heat transfer in a round impinging jet , 2008, Journal of Fluid Mechanics.

[28]  B. Geurts,et al.  A framework for predicting accuracy limitations in large-eddy simulation , 2002 .

[29]  Y. Kaneda,et al.  Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation , 2009 .

[30]  W. Habashi,et al.  2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics , 1998 .

[31]  Y. Pao.  Structure of Turbulent Velocity and Scalar Fields at Large Wavenumbers , 1965 .

[32]  Honglu Wang,et al.  The integral scale in homogeneous isotropic turbulence , 2002, Journal of Fluid Mechanics.

[33]  Uriel Frisch,et al.  A simple dynamical model of intermittent fully developed turbulence , 1978, Journal of Fluid Mechanics.

[34]  S. Orszag,et al.  Small-scale structure of the Taylor–Green vortex , 1983, Journal of Fluid Mechanics.