Mathematics of Large Eddy Simulation of Turbulent Flows

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Subgrid modelling for two-dimensional turbulence using neural networks (2018, background): “This modelling of the excluded wavenumbers in LES represents the classical closure problem which has spawned a variety of algebraic or equation based techniques for representing the eﬀect of these discarded scales on the resolved ones (Berselli et al. 2005; Sagaut 2006).”
On the energy equality for the 3D Navier–Stokes equations (2018, background): “See [6, 8], Flandoli, Gubinelli, Hairer, and Romito [24], and Kupiainen [33].”
Global attractors and determining modes for the 3D Navier-Stokes-Voight equations (2007, methodology): “The system (1.1)-(1.2) models the dynamics of a Kelvin-Voight viscoelastic incompressible fluid and was introduced by A.P. Oskolkov in [38] as a model of motion of linear, viscoelastic fluids.”
Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, background): “We note that, if filtering and differentiation do not commute, one has to estimate the commutation error (see for example Vasilyev & Goldstein 2004; Vasilyev et al. 1998; Berselli et al. 2006).”
Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows (2006, methodology): “Also, the simple formulation νT =(Cs∆) 2|S − 〈S〉| (Berselli et al. 2005) leads to Fsgs (Cs∆)2|〈S〉|2〈|S ′|〉 when |〈S〉| |S ′|, which contradicts the expression of the mean SGS energy flux.”