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

Abstract 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. A strategy 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.

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