Time Filtered Second Order Backward Euler Method for EMAC Formulation of Navier-Stokes Equations

This paper considers the backward Euler based linear time filtering method for the developed energy-momentum-angular momentum conserving (EMAC) formulation of the time dependent-incompressible Navier-Stokes equations in the case of weakly enforced divergence constraint. The method adds time filtering as a post-processing step to the EMAC formulation to enhance the accuracy and to improve the approximate solutions. We show that in comparison with the Backward-Euler based EMAC formulation without any filter, the proposed method not only leads to a 2-step, unconditionally stable and second order accurate method but also increases numerical accuracy of solutions. Numerical studies verify the theoretical findings and demonstrate preeminence of the proposed method over the unfiltered case.