Time integration as filtering: a space-time discretization-aware LES formulation

Abstract: Discretization-aware LES yields an exact expression for the discrete target flux in finite-volume LES by recognizing that a coarse finite difference is a top-hat-filtered exact derivative (the "filter-swap" property). That argument is purely spatial; here we observe that the forward-Euler time difference is itself a (one-sided) top-hat-filtered exact time derivative, and repeat the construction in space-time. The resulting exact discrete flux decomposition extends the spatial one with a single temporal term: a flux-quadrature error that shrinks with the quadrature order of the time integrator. In a Burgers experiment this term grows with the CFL number while the spatial terms do not, and a Smagorinsky closure augmented with its leading order - a Lax-Wendroff-type diffusion - stays accurate at coarse time steps where space-only closures degrade.