Structured adaptive mesh refinement using leapfrog time integration on a staggered grid for ocean models

A leapfrog time integration technique for adaptive mesh refinement (AMR) is presented and compared to single-step and multi-step two time-level integrators for a standard 2D advection test case with time-varying, but specified, refinement. Leapfrog gives error and run times comparable to those of the two time-level integrators. A second advection test case is performed to demonstrate how reflections at coarse/fine interfaces produced by leapfrog can be damped using edge smoothing. tegy for staggered grid AMR is presented with velocities defined at cell vertices and tracer and pressure variables defined at cell centres (B-grid). A barotropic modon test case using numerics from a well-documented ocean model is used to demonstrate the ability of staggered grid AMR on a geophysical application. Again refinement regions are time-varying, but specified by the analytic solution.