A geometry-based dynamically constrained sub-grid model for large-eddy simulation

A new sub-grid scale (SGS) model for large-eddy simulation (LES), referred to as the cascade-admissible geometric SGS (CAGS) model, is proposed based on an invariant representation of the local velocity gradient. The model interprets SGS activity through the geometric structure of the resolved deformation field using invariant ratios that quantify the volumetric richness of the velocity-gradient tensor. The model naturally suppresses SGS activity in laminar or rank-deficient flow configurations while remaining invariant under coordinate transformations. Since geometric degeneracy of the deformation field does not necessarily imply absence of turbulence, a cascade-admissibility mechanism preserves SGS activity when the local flow remains capable of sustaining vortex stretching and turbulent energy transfer. Correct near-wall asymptotic behavior is derived directly from the progressive rank collapse of the velocity-gradient tensor, eliminating empirical damping functions. The closure relies solely on local tensor invariants and avoids eigenvalue or singular value evaluations, making it computationally efficient and numerically robust. Performance is assessed through homogeneous isotropic turbulence decay, periodic hill flow, and zero-pressure gradient flat plate boundary layer development. Additional validation is performed for the three-dimensional asymmetric diffuser flow of Cherry et al. [“Separated flow in a three-dimensional diffuser: Preliminary validation,” in Annual Research Briefs (Centre for Turbulence Research, Stanford University, 2006)], one of the most demanding wall-bounded LES benchmarks, characterized by corner separation, secondary flow, strong adverse pressure-gradients, and low-frequency large-scale dynamics. The results indicate that the CAGS model maintains stable laminar suppression, realistic near-wall behavior, and improved prediction of separation, reattachment, and secondary flow structures relative to several established SGS closures.