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 Germano's classical dynamic procedure redefined in terms of two wavelet thresholding filters.

Keywords:

• Large Eddy Simulation
• Stochastic Coherent Adaptive Large Eddy Simulation
• Coherent Vortex Simulation
• Turbulence
• Wavelets
• Wavelet Filtering

Acknowledgments

This work was supported by the Department of Energy (DOE) under Grant No. DE-FG02-05ER25667, the National Aeronautics and Space Administration (NASA) under grant No. NAG-1-02116, the National Science Foundation (NSF) under grants No. EAR-0327269 and ACI-0242457, and the Natural Sciences and Engineering Research Council of Canada. The authors would also like to thank the Shared Hierarchical Academic Research Computing Network and the Minnesota Supercomputing Institute for providing computational resources.