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Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence. (English) Zbl 1191.76061
Summary: We study a computationally attractive algorithm (based on an extrapolated Crank-Nicolson 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 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 Crank-Nicolson method can be more accurate at higher Reynolds number that the classical extrapolated trapezoidal method of Baker (Report, Harvard University, 1976). We also show the higher order Leray-deconvolution models (e.g. N=1,2,3) have greater accuracy than the N=0 case of the Leray-α model. Numerical experiments for the 2d step problem are also successfully investigated. Around the critical Reynolds number, the low order models inhibit vortex shedding behind the step. The higher order models, correctly, do not. To estimate the complexity of using Leray-deconvolution models for turbulent flow simulations we estimate the models’ microscale.

MSC:
76F65Direct numerical and large eddy simulation of turbulence
76F02Fundamentals of turbulence
35Q35PDEs in connection with fluid mechanics
65M06Finite difference methods (IVP of PDE)
76D05Navier-Stokes equations (fluid dynamics)
76M25Other numerical methods (fluid mechanics)