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.


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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