A high-performance explicit vertical advection scheme for ocean models: how PPM can beat the CFL condition

Explicit numerical advection schemes must generally satisfy the Courant-Fri edrichs-Lewy (CFL) condition, that an advected quantity must not move more than one grid interval in one time step. This can be a very restrictive con dition in the vertical when high resolution is required in areas of upwelli ng and downwelling or in sigma-coordinate models where there is steep bathy metry and there is a high vertical transformed velocity. In this note, an e xplicit scheme which does not have this restriction is presented for vertic al advection, based on the piecewise parabolic method (PPM). It also has lo w numerical diffusion and does not introduce spurious oscillations near sha rp gradients. It is demonstrated in a number of test cases of downwelling o f various initial distributions, indicating that gradients resolved over a few grid points are advected accurately. (C) 2000 Elsevier Science Inc. All rights reserved.