Sensitivity of the scale partition for variational multiscale large-eddy simulation of channel flow

Abstract

The variational multiscale method has been shown to perform well for large-eddy simulation ͑LES͒ of turbulent flows. The method relies upon a partition of the resolved velocity field into large-and small-scale components. The subgrid model then acts only on the small scales of motion, unlike conventional LES models which act on all scales of motion. For homogeneous isotropic turbulence and turbulent channel flows, the multiscale model can outperform conventional LES formulations. An issue in the multiscale method for LES is choice of scale partition and sensitivity of the computed results to it. This is the topic of this investigation. The multiscale formulation for channel flows is briefly reviewed. Then, through the definition of an error measure relative to direct numerical simulation ͑DNS͒ results, the sensitivity of the method to the partition between large-and small-scale motions is examined. The error in channel flow simulations, relative to DNS results, is computed for various partitions between large-and small-scale spaces, and conclusions drawn from the results.

Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations

“…The method has a variational basis, as it relies on "projecting" the subgrid model onto the fine-scale motions, 10 and it was shown to outperform conventional LES models in Hughes et al 9 It appeared that extracting energy only from high wave number modes led to better results than formulations which extract energy from all modes. Subsequent studies have also confirmed the good behavior of the variational multiscale method on a variety of problems: see Hughes, Oberai, and Mazzei, 11 Winckelmans and Jeanmart, 12 Oberai and Hughes, 13 Farhat and Koobus, 14 Jeanmart and Winckelmans, 15 Holmen et al, 16 Koobus and Farhat,17 Ramakrishnan and Collis. [18][19][20][21] In this work, the spectral eddy viscosities for the conventional dynamic Smagorinsky model and the variational multiscale model are calculated and examined for a range of discretizations.…”

“…No effort has been made yet to determine optimal values of k for homogeneous isotropic flows. An initiatory study of the sensitivity of results to the ratio k / kЈ, with kЈ fixed, for channel flows is presented in Holmen et al 16 There it was observed that smaller ratios of k / kЈ ͑Ϸ0.5͒ better suited the dynamic multiscale model and larger ratios of k / kЈ ͑Ϸ0.7͒ performed better for the static multiscale model. It has not yet been determined whether this trend is generally applicable.…”

Evaluating large eddy simulation results based on error analysis

“…It is defined as the deviation of the predicted statistic Q sim x and the corresponding statistic observed by the reference Q ref x interpolated at position x. In contrast to other evaluation studies of numerical simulations [22,24,40,64], the present error measure is normalized by the difference d(.) between the maximal and minimal value of the reference data Q ref , corresponding to the interval of interest.…”

The Isogeometric Variational Multiscale Method for Laminar Incompressible Flow

“…Another interpretation for the VMS can considered as a new technique to take account the effect of neglected unresolved fine-scale onto the behavior of coarse-scale. It also has prepared a logical proof for the stabilized methods and a platform for the development of new computational technologies ( see [3,7,11,17] for application to turbulence modeling and simulation). In VMS approach to solve turbulent flow, the scale separation is carried out by means of a projection onto the finite element space.…”

“…In this work we employ the residual-based variational multiscale (RBVMS) turbulence modeling approach recently proposed in [3] (also see [5] for earlier reference). The modeling paradigm is based on the variational multiscale theory of turbulence [4,7,8,9,11] and the numerical experience of stabilized methods [4,18] that are residual-based. The VMS provides a theoretical framework for general multiscale problems in computational mechanics by separating the scales of interest in a predetermined number of groups, usually two, coarse-scale and fine-scale, three groups have been considered as well, coarse resolved scales, fine resolved scales, and unresolved scales (i.e.…”