On Bardina and Approximate Deconvolution Models

International audienceWe first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution” to the ADM for each deconvolution order N, and then that the corresponding sequence of solutions converges to the mean Navier-Stokes Equations when N goes to infinity