Can Explicit Subgrid Models Enhance Implicit LES Simulations? A Very High-Order Solver Perspective

Abstract

High-order discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent-flow simulations and are increasingly attractive on GPU-oriented architectures, where high polynomial orders can improve arithmetic intensity. However, very high-order under-resolved simulations remain sensitive to the balance between numerical and modeled dissipation. We investigate how explicit Vreman subgrid-scale (SGS) modeling interacts with dissipation from split-form stabilization and Riemann solvers in a DGSEM framework. Using the three-dimensional Taylor-Green vortex at Re=1600 and in the inviscid limit, we assess kinetic-energy dissipation, spectral accuracy, and stability across well-resolved, under-resolved viscous, and strongly under-resolved regimes, comparing lower- and very high-order configurations at similar degrees of freedom. The usefulness of explicit SGS modeling depends strongly on resolution, polynomial order, and the numerical dissipation already present. In the well-resolved cases considered, Vreman modeling does not improve accuracy because its active wavenumber range overlaps with the scheme's inherent dissipation. At similar degrees of freedom, lower-order simulations introduce stronger damping near the smallest resolved scales, whereas very high-order simulations preserve more spectral content but are more susceptible to high-wavenumber energy accumulation when dissipation is insufficient. Under stronger under-resolution, a weak SGS contribution can control this accumulation, while excessive SGS dissipation degrades intermediate scales. These results identify regimes in which explicit SGS modeling is beneficial, neutral, or detrimental, and provide practical guidance for selecting dissipation mechanisms in very high-order DG turbulence simulations suited to modern GPU architectures.