On Crank–Nicolson Adams–Bashforth timestepping for approximate deconvolution models in two dimensions

We consider a Crank–Nicolson–Adams–Bashforth temporal discretization, together with a finite element spatial discretization, for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions. We prove a restriction on the timestep that will guarantee stability, and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems.