We study a computationally attractive algorithm (based on an extrapolated CrankNickolson method) for a recently proposed family of high accuracy turbulence models (the Leray-deconvolution family). First we prove convergence of the algorithm to the solution of the Navier Stokes equations (NSE) and delineate its (optimal) accuracy. Numerical experiments are presented which confirm the convergence theory. Our 3d experiments also give a careful comparison of various related approaches. They show the combination of the Leray-deconvolution regularization with the extrapolated CrankNicolson method can be more accurate at higher Reynolds number that the classical extrapolated trapezoidal method of Baker [6]. We also show the higher order Leraydeconvolution models (e.g. N = 1, 2, 3) have greater accuracy than the N = 0 case of the Leray-alpha model. Numerical experiments for the 2-dimensional step problem are also successfully investigated, showing the higher order models have a reduced effect on transition from one flow behavior to another. To estimate the complexity of using Leraydeconvolution models for turbulent flow simulations we estimate the models' microscale.
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