subgridscale

Subgrid-scale (SGS) refers to the range of turbulent motions that lie smaller than the grid resolution in large-eddy simulation (LES). In LES, the Navier–Stokes equations are filtered to separate resolvable scales from unresolved subgrid scales. The filtering process introduces a subgrid-scale stress tensor that represents the momentum transfer from unresolved motions to the resolved flow. Since these small scales are not simulated directly, their influence must be modeled to close the equations and predict accurate transport of momentum and energy.

The most common SGS modeling approach uses an eddy-viscosity concept, where the SGS stresses are related to the resolved strain rate by an effective turbulent viscosity. This leads to models that add dissipation to mimic the energy cascade from large to small scales. The Smagorinsky model is a foundational example, with the dynamic Smagorinsky model adjusting the eddy-viscosity coefficient in space and time using the Germano identity to improve adaptability. Structural or similarity models attempt to reconstruct parts of the SGS stresses from the resolved fields and are sometimes used in combination with eddy-viscosity terms to form mixed models.

Several variants address specific challenges. WALE and Vreman models improve near-wall behavior and stability in wall-bounded flows. Dynamic models estimate coefficients locally, reducing the need for empirical calibration. Limitations of SGS modeling include sensitivity to grid resolution and filter choice, difficulties in representing backscatter (energy transfer from small to large scales), and reduced accuracy in highly anisotropic or transitional flows.

Subgrid-scale modeling remains central to LES, enabling simulations of turbulent flows in engineering, environmental, and geophysical applications with reduced computational cost relative to direct numerical simulation.