Large Eddy Simulation of Homogeneous Isotropic Turbulent Flow Using the Finite Element Method

Abstract

This paper presents results of validation study of large eddy simulation (LES) that is applied to homogeneous isotropic turbulence in order to assess its spectral accuracy. The LES is performed by using a streamline-upwind finite element method with second order accuracy both in time and space and the results are compared with those from direct numerical simulation (DNS) based on the spectral method. The validation tests are done by using Standard Smagorinsky Model (SSM) and Dynamic Smagorinsky Model (DSM), and include following two cases: a low Reynolds number case and a higher Reynolds number case. In the former case, the Reynolds number is low enough that the computational grid is capable of resolving all the turbulence scales. In this case our interest is in whether any effects of the subgrid scale (SGS) model should appropriately be dampened out. In the latter case, a relatively large Reynolds number is selected where effects of turbulent eddies that are not resolved by the computational grid should be properly taken into account by the SGS model. It is confirmed that DSM performs better than SSM for both cases and it gives good agreement with DNS results in terms of both spatial spectra and decay of the turbulence statistics. Visualization of the computed flow fields by the DSM also reveals existence of distinct, coherent and tube-like vortical structures similar to those found in instantaneous flow fields computed by the DNS.