A finite-volume variational multiscale method coupled with a discrete interpolation filter for large-eddy simulation of isotropic turbulence and fully developed channel flow

Abstract

The variational multiscale (VMS) approach proposed by Hughes et al. is applied to the Smagorinsky model and developed within the context of a physical-space unstructured finite-volume solver. A specific explicit filtering procedure is also developed, based on the idea of the discrete interpolation filters, originally proposed by Marsden et al. Tests on decaying isotropic turbulence at infinite Reynolds number and fully developed channel flow at friction Reynolds number Reτ=395 are performed, using the dynamic Smagorinsky model for comparison. For the VMS version of the Smagorinsky model, the conservative choice of not adapting the model’s constant is made, giving good indications on the required adjustment directions in both isotropic flows and nonisotropic flows. Promising results are obtained in general by the VMS approach with the two test cases. An overdissipative behavior is observed in the isotropic turbulence test case, which does not have a strong spectral connotation and could probably be cured adjusting the model’s constant. A very good prediction of the levels of unsteadiness is produced by VMS in the channel flow test case, showing the potential of this approach for nonisotropic flows. In both of the test cases the VMS approach gives performances of the same order of accuracy of the dynamic Smagorinsky model used for comparison, being at the same time less computationally expensive.