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

TL;DR

This paper investigates how explicit subgrid models interact with implicit dissipation in high-order DG methods on GPUs, revealing conditions where SGS models are beneficial or redundant in turbulence simulations.

Contribution

It provides a comprehensive analysis of the interplay between implicit DG dissipation and explicit SGS models, offering practical guidance for high-order turbulence simulations on GPU architectures.

Findings

SGS models are unnecessary when split-form DG schemes ensure stability.

Adding SGS models does not improve accuracy in well-resolved LES.

Explicit SGS models help at high Reynolds numbers with insufficient resolution.

Abstract

High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations, especially when implemented on GPU-oriented architectures that favor very high polynomial orders. On modern GPUs, high-order polynomial evaluations cost roughly the same as low-order ones, provided the DG degrees of freedom fit within device memory. However, even with high-order discretizations, simulations at high Reynolds numbers still require some level of under-resolution, leaving them sensitive to numerical dissipation and aliasing effects. Here, we investigate the interplay between intrinsic DG dissipation mechanisms (implicit dissipation) -- in particular split forms and Riemann solvers -- and explicit subgrid-scale models in Large Eddy Simulations (LES). Using the three-dimensional Taylor--Green vortex at $Re = 1600$ and an inviscid case ($Re \to \infty$), we evaluate kinetic energy dissipation, spectral accuracy, and numerical stability. Our results show that when stability for under-resolved turbulence is ensured through split-forms (energy- or entropy-stable) schemes, subgrid-scale (SGS) LES models are not strictly necessary. At moderate Reynolds numbers, when the spatial resolution is sufficient to capture the relevant turbulence scales (i.e., in well-resolved LES), adding SGS models does not improve accuracy because the wavenumber range where they act overlaps with the inherent numerical dissipation of the DG scheme. In contrast, when the resolution is insufficient, as is typical at high Reynolds numbers, explicit subgrid-scale models complement the numerical dissipation and enhance accuracy by removing the excess energy that numerical fluxes alone cannot dissipate. These findings provide practical guidance for choosing numerical strategies in high-order turbulence simulations.