A Dynamic Transport Equation for Large Eddy Simulation Subgrid Closure

Abstract

Large Eddy Simulation (LES) relies on subgrid-scale (SGS) closure models to represent unresolved stresses. Many common eddy-viscosity closures are algebraic and effectively assume near-instantaneous local equilibrium between production and dissipation, an assumption that can degrade performance in transitional and non-equilibrium regimes. Here we use sparse symbolic regression on filtered Taylor-Green vortex (TGV) reference data to infer a compact evolution law for the SGS eddy-viscosity coefficient. The resulting model is a one-equation temporal-relaxation update , C n+1 = αC n + β |S n | |Ω n |, which combines explicit memory with a vortex-stretching-inspired production term. When coupled back into a finite-difference LES solver with a non-negative dissipation safeguard, the model remains stable and self-regulating across decaying turbulence and driven channel flow without retuning. In an a posteriori TGV benchmark against a higher-resolution pseudo-spectral DNS reference, the proposed closure tracks the DNS kinetic-energy decay more closely than Smagorinsky and WALE under matched numerical settings. On the TGV energy-decay benchmark, the proposed closure reduces normalized RMSE by 23% relative to WALE and 36% relative to Smagorinsky. Furthermore, spectral analysis confirms that while the model exhibits a slight lag during the initial breakdown due to temporal inertia, it reproduces the DNS kinetic energy spectrum with higher fidelity than standard models in the fully developed and decaying regimes.