A TWO-LEVEL MULTISCALE DECONVOLUTION METHOD FOR THE LARGE EDDY SIMULATION OF TURBULENT FLOWS

This report presents a novel continuous deconvolution method which is used to solve the closure problem in Large Eddy Simulation (LES for short) leading to a new LES model. In the deconvolution method described herein the flow velocities u are approximated by their average ũ on a fine intermediate length scale γ and then, by means of an exact extrapolation formula, expressed in terms of the averaged flow ū on the length scale α, which we seek to resolve. We prove existence, uniqueness and regularity of the weak solution w(α, γ) of the resulting LES models as well as energy estimates of the weak solution that are uniform in the intermediate length scale γ of the deconvolution procedure. We show also that the modeling error ‖ū - w(α, γ)‖ is driven only by the deconvolution error ‖u - ũ‖ and is independent of the resolved scale α.