Daniel E. Goldstein

Stochastic Coherent Adaptive Large Eddy Simulation Method

In this paper we propose a novel approach called the stochastic coherent adaptive large eddy simulation (SCALES) method which takes advantage of both the coherent vortex simulation (CVS) and large eddy simulation (LES) methods. With the SCALES method a wavelet filter is applied to a turbulent field such that the maximum number of modes are resolved in the simulation, given the balance between computing resources and user defined acceptable simulation error. As with CVS, the wavelet thresholding filter will allow a SCALES simulation to resolve and “track” the coherent energetic structures in a turbulent flow field. The wavelet filter compression in SCALES will be substantially greater than the “ideal” wavelet compression used in CVS, making it cost effective for simulating high Re number flows. The SCALES methodology will simulate the most important modes given the resources available. Because of the higher wavelet compression the subgrid scales (SGS) in a SCALES simulation will contain both coherent and i...

CVS and SCALES simulation of 3-D isotropic turbulence

In this work coherent vortex simulation (CVS) and stochastic coherent adaptive large eddy simulation (SCALES) simulations of decaying incompressible isotropic turbulence are compared to DNS and large eddy simulation (LES) results. Current LES relies on, at best, a zonally adapted filter width to reduce the computational cost of simulating complex turbulent flows. While there is an improvement over a uniform filter width, this approach has two limitations. First, it does not capture the high wave number components of the coherent vortices that make up the organized part of turbulent flows, thus losing essential physical information. Secondly, the flow is over-resolved in the regions between the coherent vortices, thus wasting computational resources. The SCALES approach addresses these shortcomings of LES by using a dynamic grid adaptation strategy that is able to resolve and track the most energetic coherent structures in a turbulent flow field. This corresponds to a dynamically adaptive local filter width. Unlike CVS, which we show is able to recover low order statistics with no subgrid scale (SGS) stress model, the higher compression used in SCALES necessitates that the effect of the unresolved SGS stresses must be modeled. These SGS stresses are approximated using a new dynamic eddy viscosity model based on Germanos classical dynamic procedure redefined in terms of two wavelet thresholding filters.

Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation

Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most “energetic” coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible...

On the role of subgrid-scale coherent modes in large-eddy simulation

The role of coherent and incoherent subgrid-scale modes in large-eddy simulation modelling is examined. The coherent/incoherent decomposition of the subgrid-scale stresses based on the wavelet de-noising procedure is introduced. Ap rioridynamical tests based on the perfect modelling approach are performed for decaying isotropic turbulence. The theoretical effects of coherent and incoherent subgrid-scale forces are dynamically evaluated during the simulation. The relation between deterministic/ stochastic subgrid-scale models and coherent/incoherent subgrid-scale stresses is discussed. The main result is that in large-eddy simulations low-order statistics can be almost exactly reproduced when only the effect of the coherent subgrid-scale modes is accounted for, while the incoherent subgrid-scale modes have a negligible effect upon the large-scale dynamics and the energy transfer.

Lagrangian dynamic SGS model for stochastic coherent adaptive large eddy simulation

Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of large eddy simulation that uses a wavelet filter-based dynamic grid adaptation strategy to solve for the most energetic coherent structures in a turbulent flow field, while modeling the effect of the less energetic ones. A localized dynamic subgrid scale model is needed to fully exploit the ability of the method to track coherent structures. In this paper, new local Lagrangian models based on a modified Germano dynamic procedure, redefined in terms of wavelet thresholding filters, are proposed. These models extend the original path-line formulation of Meneveau et al. [J. Fluid Mech. 319 (1996)] in two ways: as Lagrangian path-line diffusive and Lagrangian path-tube averaging procedures. The proposed models are tested for freely decaying homogeneous turbulence with initial Re λ = 72. It is shown that the SCALES results, obtained with less than 0.4% of the total non-adaptive nodes required for a DNS with the same wavelet solver, closely match reference DNS data. In contrast to classical LES, this agreement holds not only for large scale global statistical quantities, but also for energy and, more importantly, enstrophy spectra up to the dissipative wavenumber range.

A THREE-DIMENSIONAL ADAPTIVE WAVELET METHOD FOR FLUID-STRUCTURE INTERACTION

An adaptive wavelet collocation method for three-dimensional fluid-structure interaction at large Reynolds numbers is presented. This approach is shown to give accurate results with a reduced number of computational elements. The method is applied to two-dimensional flow past moving and fixed cylinders at Re = 102 and Re = 104, and to three-dimensional flow past a sphere at Re = 500. This is the first three-dimensional calculation of a flow past an obstacle using a dynamically adapted wavelet based approach.

Local spectrum of commutation error in large eddy simulations

In this Brief Communication we present a new mathematical tool, which we call local spectrum analysis, that can be used to obtain information about local spectral content of the commutation error in large eddy simulations and its dependence on the filter shape and the non-uniformity of the filter width. To illustrate these theoretical findings, the local commutation spectrum analysis is applied to the results of 2563 direct numerical simulation of forced homogeneous turbulence at Reλ=168. The results confirm strong dependence of the spectral content of the commutation error on the filter shape: the spectrum is wide for smooth filters like Gaussian, while for filters, that are close to the sharp cut-off, the spectral content is localized. It is also demonstrated that the amplitude of the commutation error is linearly proportional to the filter width stretching factor.

Towards Lagrangian dynamic SGS model for SCALES of isotropic turbulence

1 Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universita di Napoli, 81031 Aversa, Italy (giuliano.destefano@unina2.it) 2 Department of Mechanical Engineering, University of Colorado at Boulder, 427 UCB, Boulder CO, USA (Daniel.E.Goldstein@colorado.edu, Oleg.Vasilyev@colorado.edu) 3 Department of Mathematics & Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1 (kevlahan@mcmaster.ca)

A-priori dynamic test for deterministic/stochastic modeling in large-eddy simulation of turbulent flow

The coherent/incoherent decomposition of the subgrid-scale stresses based on the wavelet de-noising procedure is exploited in the framework of large-eddy simulation of turbulence. Dynamic a-priori tests based on the perfect modeling approach are performed for decaying isotropic turbulence. The theoretical performances of deterministic/stochastic subgrid-scale models are evaluated during the simulation. The main result is that in large-eddy simulations low order statistics can be almost exactly reproduced when only the effect of the coherent subgrid-scale modes is accounted for, while the incoherent subgrid-scale stresses not affecting the energy transfer.