Comparison of Sub-Grid Scale Models for Large-Eddy Simulation Using a High-Order Spectral Element Approximation of the Compressible Navier-Stokes Equations at Low Mach Number

This study investigates the properties and performance of different sub-grid scale (SGS) models for the large eddy simulation (LES) of low Mach compressible flows using high-order spectral elements. We compare the classical Smagorinsky-Lilly and Vreman models against two dynamic SGS (DSGS) variants: a time-dependent residual-based model (R-DSGS) and a time-independent version (T-DSGS). These models are evaluated based on numerical stability, extrema minimization, discontinuity preservation, and energy transfer across scales. Benchmarks include passively advected tracers, nonlinear systems with discontinuities, gravity-driven stratified flows, and homogenous isotropic turbulence. All models effectively preserve sharp discontinuities, though Vreman and both DSGS variants more significantly reduce oscillations in advection problems. For high-order spectral element stability, R-DSGS and T-DSGS prove more robust than Smagorinsky or Vreman. While Smagorinsky and Vreman better resolve fine-scale structures in shear flows, the nodal R-DSGS implementation exhibits superior energy conservation. Overall, the nodal R-DSGS model outperforms the other candidates across most metrics—particularly compared to its element-based counterpart—and remains on par regarding the others. This suggests R-DSGS is a highly effective model for stabilizing transport-dominated problems in high-order spectral element frameworks.