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33
A spectral vanishing viscosity method for largeeddy simulations
 J. Comput. Phys
"... A new simulation approach for high Reynolds number turbulent flows is developed, combining concepts of monotonicity in nonlinear conservation laws with concepts of largeeddy simulation. The spectral vanishing viscosity (SVV), first introduced by E. Tadmor [SIAM J. Numer. Anal. 26, 30 (1989)], is in ..."
Abstract

Cited by 24 (2 self)
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A new simulation approach for high Reynolds number turbulent flows is developed, combining concepts of monotonicity in nonlinear conservation laws with concepts of largeeddy simulation. The spectral vanishing viscosity (SVV), first introduced by E. Tadmor [SIAM J. Numer. Anal. 26, 30 (1989)], is incorporated into the Navier– Stokes equations for controlling highwavenumber oscillations. Unlike hyperviscosity kernels, the SVV approach involves a secondorder operator which can be readily implemented in standard finite element codes. In the work presented here, discretization is performed using hierarchical spectral/hp methods accommodating effectively an ab initio intrinsic scale separation. The key result is that monotonicity is enforced via SVV leading to stable discretizations without sacrificing the formal accuracy, i.e., exponential convergence, in the proposed discretization. Several examples are presented to demonstrate the effectiveness of the new approach including a comparison with eddyviscosity spectral LES of turbulent channel flow. In its current implementation the SVV approach for controlling the small scales is decoupled from the large scales, but a procedure is proposed that will provide coupling similar to the classical LES formulation. c ○ 2000 Academic Press 1.
Spectra of Local and Nonlocal Twodimensional Turbulence
, 1994
"... We propose a family of twodimensional incompressible fluid models indexed by a parameter o~e[0,~], and discuss the spectral scaling properties for homogeneous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spec ..."
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Cited by 12 (2 self)
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We propose a family of twodimensional incompressible fluid models indexed by a parameter o~e[0,~], and discuss the spectral scaling properties for homogeneous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spectrally local for o ~ < 2, but becomes dominated by nonlocal interactions for cr> 2. Numerical simulations indicate that the spectral slopes are systematically steeper than those predicted by the local scaling argument.
A Fractal Model for Large Eddy Simulation of Turbulent Flow
, 1999
"... A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgridscale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down ..."
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Cited by 10 (1 self)
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A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgridscale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the approach is used in the context of the coarsegrained Burgers equation. Then, fractal interpolation is extended to three dimensions and is used to formulate a subgrid model for the filtered NavierStokes equations. The model is applied to LES of both steady and freely decaying isotropic turbulence. We find that the assumption of fractality per s e is not enough to yield physically meaningful results, and we explore several variants of the model in which the rules to generate the synthetic fields explicitly incorporate the condition that energy dissipation take place. In one dimension, this is accomplished by means of an additional transport equation that allows to dynamically determine the fractal dimension. In three dimensions, good results are obtained only once the fractal dimension is allowed to vary in different eigendirections of the resolved strainrate tensor so as to (nearly) maximize energy dissipation. c #1999 Elsevier Science B.V. All rights reserved. Keywords: Large eddy simulation; Fractal; Turbulence modeling 1.
Compressible Large Eddy Simulation Using Unstructured Grid: Supersonic Boundary Layer And Compression Ramps
, 2000
"... A Mach 3 adiabatic at plate turbulent boundary layer at Re = 2 10 4 is studied using the Monotone Integrated Large Eddy Simulation (MILES) method. The Favreltered compressible NavierStokes equations are solved on a threedimensional unstructured grid of tetrahedral cells. A variable limiter den ..."
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Cited by 9 (1 self)
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A Mach 3 adiabatic at plate turbulent boundary layer at Re = 2 10 4 is studied using the Monotone Integrated Large Eddy Simulation (MILES) method. The Favreltered compressible NavierStokes equations are solved on a threedimensional unstructured grid of tetrahedral cells. A variable limiter denoted the extremum limiter is developed to control the overshoots caused by high order interpolation. The statistical predictions computed with and without the limiter are compared with experimental data and Direct Numerical Simulation (DNS). Results for 8 and 25 compression corners at Mach 3 and Re = 2 10 4 are compared with experimental data. 1 Introduction High order Total Variation Diminishing (TVD) schemes have been developed in one dimension into reliable tools for numerical prediction of the solution of hyperbolic systems of equations. However, in higher dimensions it has proved dicult to obtain the same degree of robustness and accuracy with extensions of these one dim...
Turbulence Noise
"... We show that the largeeddy motions in turbulent fluid flow obey a modified hydrodynamic equation with a stochastic turbulent stress whose distribution is a causal functional of the largescale velocity field itself. We do so by means of an exact procedure of "statistical filtering" of the NavierSt ..."
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Cited by 5 (2 self)
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We show that the largeeddy motions in turbulent fluid flow obey a modified hydrodynamic equation with a stochastic turbulent stress whose distribution is a causal functional of the largescale velocity field itself. We do so by means of an exact procedure of "statistical filtering" of the NavierStokes equations, which formally solves the closure problem, and we discuss relations of our analysis with the "decimation theory" of Kraichnan. We show that the statistical filtering procedure can be formulated using fieldtheoretic pathintegral methods within the MartinSiggiaRose formalism for classical statistical dynamics. We also establish within the MSR formalism a "leasteffectiveaction principle" for mean turbulent velocity profiles, which generalizes Onsager's principle of least dissipation. This minimum principle is a consequence of a simple realizability inequality and therefore holds also in any realizable closure. Symanzik's theorem in fieldtheorywhich characterizes the sta...
Experimental and numerical studies of an eastward jet over topography
, 2000
"... Motivated by the phenomena of blocked and zonal flows in Earth’s atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumbertwo topography. The laboratory experiments studied the dynamical behaviour of the flow in a baro ..."
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Cited by 5 (1 self)
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Motivated by the phenomena of blocked and zonal flows in Earth’s atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumbertwo topography. The laboratory experiments studied the dynamical behaviour of the flow in a barotropic rotating annulus as a function of the experimental Rossby and Ekman numbers. Two distinct flow patterns, resembling blocked and zonal flows in the atmosphere, were observed to persist for long time intervals. Earlier model studies had suggested that the atmosphere’s normally upstreampropagating Rossby waves can resonantly lock to the underlying topography, and that this topographic resonance separates zonal from blocked flows. In the annulus, the zonal flows did indeed have superresonant mean zonal velocities, while the blocked flows appear subresonant. Lowfrequency variability, periodic or irregular, was present in the measured time series of azimuthal velocity in the blocked regime, with dominant periodicities in the range of 6–25 annulus rotations. Oscillations have also been detected in zonal states, with smaller amplitude and similar frequency.
Nonlocality and Intermittency in 3D Turbulence
, 2008
"... Numerical simulations are used to determine the influence of the nonlocal and local interactions on the intermittency corrections in the scaling properties of 3D turbulence. We show that neglect of local interactions leads to an enhanced smallscale energy spectrum and to a significantly larger num ..."
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Cited by 4 (2 self)
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Numerical simulations are used to determine the influence of the nonlocal and local interactions on the intermittency corrections in the scaling properties of 3D turbulence. We show that neglect of local interactions leads to an enhanced smallscale energy spectrum and to a significantly larger number of very intense vortices (“tornadoes”) and stronger intermittency (e.g. wider tails in the probability distribution functions of velocity increments and greater anomalous corrections). On the other hand, neglect of the nonlocal interactions results in even stronger smallscale spectrum but significantly weaker intermittency. Thus, the amount of intermittency is not determined just by the mean intensity of the small scales, but it is nontrivially shaped by the nature of the scale interactions. Namely, the role of the nonlocal interactions is to generate intense vortices responsible for intermittency and the role of the local interactions is to dissipate
Direct numerical simulation tests of eddy viscosity in two dimensions, Phys. Fluids 6
, 1994
"... Twoparametric eddy viscosity (TPEV) and other spectral characteristics of twodimensional (2D) turbulence in the energy transfer subrange are calculated from direct numerical simulation (DNS) with 5122 resolution. The DNSbased TPEV is compared with those calculated from the test field model (TFM) ..."
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Cited by 3 (1 self)
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Twoparametric eddy viscosity (TPEV) and other spectral characteristics of twodimensional (2D) turbulence in the energy transfer subrange are calculated from direct numerical simulation (DNS) with 5122 resolution. The DNSbased TPEV is compared with those calculated from the test field model (TFM) and from the renormalization group (RG) theory. Very good agree1 ment between all three results is observed. Typeset using REVTEX 2 Twodimensional incompressible turbulent flows are described by the vorticity equation: ∂ζ ∂t + ∂ (∇−2 ζ, ζ) ∂(x, y) = ν0 ∇ 2 ζ, (1) where ζ is fluid vorticity and ν0 is molecular viscosity. It is well known that the existence of inviscid invariants ∫ d 2 xζ 2n of (1) results in the flux of energy towards the largest spatial scales. The presence of this inverse cascade complicates the largescale description of 2D
LargeEddy and Direct Simulation of Turbulent Flows
"... Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Simulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Objectives and plan . . . . . . . . . . . . . . . . . . . . ..."
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Cited by 3 (0 self)
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Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Simulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Objectives and plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Problem formulation 5 2.1 The NavierStokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The ltered NavierStokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Numerical methods 9 3.1 Resolution requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.1 Direct simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.2 Largeeddy simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Time advancement . . . . . . . . . . . . . . . . . . .