Numerical analysis of Leray-Tikhonov deconvolution models of fluid motion

This report develops and studies a new family of NSE-regularizations, Tikhonov Leray Regularization with Time Relaxation Models. This new family of turbulence models is based on a modification (consistent with the large scales) of Tikhonov-Lavrentiev regularization. With this approach, we obtain an approximation of the unfiltered solution by one filtering step. We introduce the modified Tikhonov deconvolution operator and study its mathematical properties. We also perform rigorous numerical analysis of a computational attractive algorithm for the considered family of models. Numerical experiments that support our theoretical results are presented.