A-priori testing of alpha regularisation models as subgrid-scale closures for large-eddy simulations

Abstract

Alpha-type regularisation models provide theoretically attractive subgrid-scale closure approximations for large-eddy simulations of turbulent flow. We adopt the a-priori testing strategy to study three different alpha regularisation models, namely the Navier–Stokes-α model, the Leray-α model, and the Clark-α model. Specifically, we use high-resolution direct numerical simulation data of homogeneous isotropic turbulence to compute the mean subgrid-scale dissipation, the spatial distribution of the subgrid-scale dissipation, and the spatial distribution of elements of the subgrid-scale stress tensor. This is done for different filter parameters and different large-eddy simulation grid resolutions. Predictions of the three regularisation models are compared to the exact values of the subgrid-scale stress tensor, as defined in the filtered Navier–Stokes equations. The potential of the three regularisation models to provide good approximations is quantified using spatial correlation coefficients. Whereas the Clark-α model exhibits the highest spatial correlation coefficients for the subgrid-scale dissipation and the subgrid-scale stress tensor elements, the Leray-α model provides lower correlation coefficients, and the Navier–Stokes-α model exhibits the lowest correlation coefficients of the three models. Our results indicate the presence of an optimal choice of the filter parameter α depending on the large-eddy simulation grid resolution.

Keywords:

• large-eddy simulation
• turbulence modelling
• subgrid-scale
• homogeneous turbulence
• isotropic turbulence

Acknowledgements

D.F. Hinz acknowledges the partial support of the Antje Graupe Pryor Foundation and the Graduate Travel Funding Program (GTFP) award of the Department of Mechanical Engineering at McGill University along with the hospitality of the Department of Mechanical Engineering at University of Washington. J.J. Riley acknowledges the support of the NSF grant OCI-0749209. E. Fried acknowledges support from the US Department of Energy and the Canada Research Chairs programme.