Dynamic Modal Filtering for Turbulence Modeling in Spectral Element Method

The lack of numerical dissipation in high-order spectral element methods has led to the development of new methods to introduce artificial dissipation. These techniques can serve both shock capturing and turbulence modelling purposes. In this study, dynamic explicit modal filtering is introduced to isolate the effects of sub-grid scale motions in under-resolved turbulent regions and enable the large-eddy simulation of turbulent flows. This filtering detects under-resolved areas through the instantaneous comparison of the local Kolmogorov length scale and the average grid spacing, then directly dissipates the excess energy by applying a modal low-pass filter on flow variables. The individual elemental operations in spectral-element method provides modes individually for each element and the filtering is applied separately for each element. The filtering intensity for under-resolved elements is adjusted based on the intensity of turbulence and the degree of under-resolvedness. The proposed filtering methodology shows high efficiency for the simulation of several benchmark turbulent flows.