Large-eddy simulation filters the Navier-Stokes equations to remove small-scale motion, then models the effect of the removed scales on the retained ones. The filtering produces a subgrid-scale stress tensor that must be modeled — this is the closure problem.
Prakash, Esmaily, and Vignon-Clementel identify a subtle inconsistency in the standard approach. The convective term in the filtered equations involves the product of two filtered quantities. Expanding this product creates Fourier modes at wavenumbers higher than the filter cutoff — modes that the filtering was supposed to remove. The standard closure ignores this inconsistency, modeling only the subgrid stress while allowing the convective term to reintroduce the very scales the filter was designed to eliminate.
The fix: a series expansion of the filtered convective term that accounts for the aliasing. The first-order correction adds a term proportional to the filter width squared times the Laplacian of the velocity product — a diffusion-like correction that removes the inconsistent high-frequency content. Higher-order corrections add higher derivatives.
The corrected LES produces better energy spectra without requiring flux limiters or other ad hoc stabilization techniques. The energy pile-up at the cutoff wavenumber — a well-known artifact of standard LES — is reduced because the inconsistent modes that caused the pile-up are no longer generated.
A foundational assumption of turbulence modeling, questioned and corrected. The filter that was supposed to clean the equations was leaving dirt behind. Cleaning up the cleanup produces better physics.