On the Stolz-Adams Deconvolution Model for the Large-Eddy Simulation of Turbulent Flows

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, pp. 21-41], [Phys. Fluids, 11 (1999), pp. 1699-1701]. 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 $\left\|{ \bf \overline{u}- w }\right\|$, where ${\bf w}$ is the model's solution and ${\bf \overline u }$ is the true flow averages.