On the convergence rates for the three‐dimensional filtered Boussinesq equations

Abstract

In this paper we consider a LES model for the approximation of large scales of the 3D Boussinesq equations. We analyze the convergence rate, in appropriate norms, of the unique regular weak solution of the regularized Boussinesq equations towards a weak solution of the original Boussinesq system.

On the exact controllability of a Galerkin scheme for 3D viscoelastic fluids with fractional Laplacian viscosity and anisotropic filtering

“…Among the others, the large eddy simulation (LES) community has manifested interest in models involving such a kind of filtering procedure (see, e.g., Refs. [2,7,12,[14][15][16][17][18]55]) and, in particular, the connection between anisotropic 𝛼-models and turbulence has been investigated by Berselli in Ref. [9] for the 3D Navier-Stokes equations, even if, in fact, the first use of anisotropic filters in turbulence dates back to the approach of Germano [29] (see also Refs.…”