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On the Stolz–Adams deconvolution model for the large-eddy simulation of turbulent flows. (English) Zbl 1128.76029

Summary: We consider a family of large-eddy simulation (LES) models with an arbitrarily high consistency error \(O(\delta^{2N+2})\) for \(N = 1,2,3,\ldots\) that are based on the van Cittert deconvolution procedure. This family of models has been proposed and tested for LES with success by Adams and Stolz in a series of papers, e.g., [Deconvolution methods for subgrid-scale approximation in large-eddy simulation, in: Modern Simulation Strategies for Turbulent Flow, R. T. Edwards, Philadelphia 2001, 21–41 (2001), An approximate deconvolution procedure for large eddy simulation, Phys. Fluids A 11, 1699–1701 (1999)]. We show that these models have an interesting and quite strong stability property. Using this property we prove an energy equality, existence, uniqueness, and regularity of strong solutions and give a rigorous bound on the modeling error \(\left\|{\overline{u}-w}\right\|\), where \({\mathbf w}\) is the model’s solution and \(\overline u\) is the true flow averages.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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