Eulerian Coherent Structure Sub-Grid Model (ECSM) for Large Eddy Simulation

Abstract

This paper introduces a new mathematical formulation to Large Eddy Simulation (LES) sub-grid scale (SGS) modeling: the Eulerian Coherent Sub-Grid Model (ECSM). The presented formulation attempts to replace the instantaneous, algebraic calculation of eddy viscosity found in classical models with a deterministic Eulerian scalar field that tracks sub-grid flow intermittency. By treating sub-grid coherent structures as a transportable volume fraction (φ), the ECSM introduces flow memory, allowing turbulence to naturally advect, diffuse, and decay based on bulk flow history. Production is driven by the second invariant of the velocity gradient tensor (the Q-criterion) to intrinsically preserve attached laminar boundary layers without empirical wall-damping functions. Destruction is formulated by translating the Lagrangian geometric collapse trajectory of a coherent structure under local strain into a Eulerian volumetric drain rate. The model baseline empirical constants have been calibrated against a 0D volume-averaged Taylor-Green Vortex, establishing a foundation for future 3D spatial testing.