Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows

This paper presents new analytical results and the first numerical results for a recently proposed multiscale deconvolution model (MDM) recently proposed. The model involves a large-eddy simulation closure that uses a novel deconvolution approach based on the introduction of two distinct filtering length scales. We establish connections between the MDM and two other models, and, on the basis of one of these connections, we establish an improved regularity estimate for MDM solutions. We also prove that the MDM preserves Taylor-eddy solutions of the Navier-Stokes equations and therefore does not distort this particular vortex structure. Simulations of the MDM are performed to examine the accuracy of the MDM and the effect of the filtering length scales on energy spectra for three-dimensional homogeneous and isotropic flows. Numerical evidence for all tests clearly indicates that the MDM gives very accurate coarse-mesh solutions and that this multiscale approach to deconvolution is effective.