Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

ABSTRACT

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re _τ = 590) and flow over a cylinder (Re _D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.

KEYWORDS:

• Large eddy simulation
• residual-based variational multiscale method
• dynamic Smagorinsky eddy-viscosity model
• combined dynamic model
• localised version of variational Germano identity

Acknowledgements

We would like to thank Dr Assad Oberai (RPI) for useful discussions on the variational Germano identity. We would also like to acknowledge the computational resources used in this study that were provided by Rensselaer's Center for Computational Innovations (CCI) and National Science Foundation's Extreme Science and Engineering Discovery Environment (XSEDE). We would like to acknowledge that meshing capabilities were provided by Simmetrix, Inc.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is funded in part by National Science Foundation's CAREER grant [grant number 1350454] and the Department of Energy, Office of Science's SciDAC-III Institute as part of the Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) program [grant number DE-SC0006617].