Longer time accuracy for the Ladyzhenskya model with the EMAC formulation

Abstract: In this paper, we incorporate the EMAC formulation into the Ladyzhenskaya model (LM), a large eddy simulation (LES) of incompressible flows. The EMAC formulation, which conserves energy, linear momentum, and angular momentum even with weak enforcement of incompressibility, has been shown to provide tangible benefits over the popular skew-symmetric for direct numerical simulation and regularized models of the Navier Stokes equations (NSE). The combination of EMAC with the LM addresses the known over-dissipation issues associated with the classical Smagorinsky model (SM). We develop a finite element discretization for the EMAC-LM system and analyze its stability and derive numerical error estimates, showing improved long-time behavior compared to the standard LM approach, particularly due to EMAC's favorable Gronwall constant independent of the Reynolds number. Benchmark simulations demonstrate that the EMAC-LM model yields more accurate flow structures, especially at high Reynolds numbers.