Numerical analysis and testing of a stable and convergent finite element scheme for approximate deconvolution turbulence models

This report presents a stable and convergent finite element scheme for the approximate deconvolution turbulence models (ADM). The ADM is a popular turbulence model intensely studied lately but the computation of its numerical solution raises issues in terms of efficiency and accuracy. This report addresses this question. The proposed scheme presented herein is based on a new interpretation of the ADM model recently introduced by the author. Following this interpretation, the solution of the ADM is viewed as the average of a perturbed Navier-Stokes system. The scheme uses the Crank-Nicolson time discretization and the finite element spatial discretization and is proved to be stable and convergent provided a moderate choice of the time step is made. Numerical tests to verify the convergence rates and performance on a benchmark problem are also provided and they prove the correctness of this approach to numerically solve the ADM.