Modal explicit filtering for large eddy simulation in discontinuous spectral element method

Developing a turbulence model that is computationally inexpensive and compatible with the nature of the numerical scheme is a crucial step in expanding the application of spectral element methods for large eddy simulation (LES) in complex geometries. In this paper, an element-level modal low-pass explicit filtering procedure, which operates in the spectral space, is implemented in a discontinuous spectral element method (DSEM). The application of the modal filter is studied for LES without a subgrid-scale (SGS) model. The method is tested for a configuration featuring isotropic turbulence, and its performance is compared with a previously used method—a spectral interpolation-based nodal filter. The modal filter shows superior performance over the nodal filter. The filtering procedure is then applied to a turbulent channel flow at a friction Reynolds number of ${\mathrm{Re}}_{\tau }=544$, and the results are compared with a previous direct numerical simulation (DNS). It is also shown that the filter strength that provides the best comparison with DNS depends only on the polynomial order and is not a function of the grid resolution. An anisotropic version of the modal filter, which damps high-frequency modes in a specific direction, is also introduced and tested for the channel flow. It is observed that filtering in the spanwise direction is the most effective approach based on the comparison of velocity mean and fluctuations with DNS. In general, the modal filter has shown good performance for both isotropic and wall-bounded flows; the calculated channel friction Reynolds number for the modal filter is within 0.26% error with respect to the DNS data, compared to 5.8% error for a case with no filtering.