Higher-order optimized hybrid Robert-Asselin type time filters

Abstract

In this paper, a class of optimized filters based on hybrid blending of implicit and explicit filters are formulated for the three time-level leapfrog time integration scheme. As the leapfrog method is the most recurrently employed in ocean and atmospheric simulations, however, it also admits a spurious mode in the numerical computations. To subdue the computational mode, the developed hybrid time filters are also optimized using constraints arising from error dynamics. The optimized filters are adept in suppressing the computational mode(s) more efficaciously without altering the physical mode. Finally, the developed hybrid filters coupled with centered and compact spatial discretization schemes are also authenticated for the numerical solutions to one-dimensional (1D) convection equation, two-dimensional (2D) dispersive rotating shallow water equation, and unsteady 2D incompressible Navier-Stokes equation at different Reynolds numbers. Present solutions are also compared with results reported in the literature.