A mathematical study of an approximate deconvolution eddy viscosity fluid model

Abstract This report investigates the mathematical properties of a novel Smagorinsky-type fluid flow model whose artificial viscosity term is obtained using filtering and approximate deconvolution. This new model has three very important properties that make it unique in its class: it is mathematically well-posed, its eddy-viscosity term is physically sound and compelling, and, unlike other models based on filtering and deconvolution, the model allows simple and efficient numerical schemes for finite element computations. Interestingly, the eddy viscosity term of the proposed model is monotone and this leads to the well-posedness of the model and its convergence to the strong solution of Navier–Stokes system as the filter radius converges to 0. Herein we present the derivation of the model and its mathematical properties.