Variational Multiscale Modeling for Turbulence Control

Abstract

We explore the capabilities of the variational multiscale (VMS) method in the context of turbulence control by applying VMS to the simulation of a simple opposition control strategy for turbulent channel flow with the results compared to prior direct numerical simulations and large-eddy simulations (LES). In all cases, the VMS method is found to be more efficient and more accurate than traditional LES with the dynamic subgrid-scale model. The simplicity, accuracy, and generality of VMS makes it particularly attractive for turbulence control investigations.

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

“…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. The spectral eddy viscosity is decomposed into terms associated with Reynolds-type interactions, crossstress interactions, and the model.…”

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

“…Additionally in VMS, the partition L e that separates the resolved scales as large and small is required. This is a crucial parameter that determines the accuracy of VMS simulations [89,90,129,133]. Here, we have demonstrated that a 4×4 planar mesh using p = 5 is sufficient to produce results with no obvious adverse effects of numerical dissipation.…”

“…The authors are not aware of any VMS implementation that has not employed some form of dealiasing. Therefore, preventing the adverse effects of aliasing errors on the large scales is necessary to obtain results that are comparable with prior VMS implementations [89,90,123,129,133].…”

“…To be more explicit, the VMS approach to LES introduces no explicit modeling on the largest resolved scales, a feature attributed to its success [89,90,123,129,133], while a SGS scale model is active on the smallest resolved scales. This can be thought of as coupling of "DNS" or no-model on the large scales with a SGS model on the small scales.…”

Variational multiscale turbulence modelling in a high order spectral element method

“…This provides us with an attractive framework for model development in which the numerical errors can be controlled, such that the true performance of the model can be assessed. The first implementations of the variational multiscale LES method [2,3,4] used global spectral methods. These methods naturally employ an orthogonal modal basis, such that the scale partitioning becomes straightforward.…”