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

摘要

Explicit numerical addiction schemes must generally satisfy the Courant-Friedrich-Lewy (CFL) condition, that an advocated quantity must not move than one grid interval in one time step. This can be a very restrictive condition in the vertical when high resolution is required in areas of upwelling and down welling or in σ-coordinate models where there is steep bathymetry and there is a high vertical transformed velocity. In this note, an explicit scheme which does not have this restriction is presented for vertical addiction, based on the piecewise parabolic method (PPM). It also has low numeral diffusion and does not introduce spurious oscillations near sharp gradients. It is demonstrated in a number of test cases of downwelling of various initial distributions, indicating that gradients resolved over a few grid points are advocated accurately.