On Nonstaggered Rectangular Grids Using Streamfunction and Velocity Potential or Vorticity and Divergence

Abstract

Dispersion characteristics of the shallow water gravity?inertia waves are discussed for two nonstaggered rectangular grids that use the velocity potential and streamfunction, and the divergence and vorticity, respectively. It is shown that the simplest second-order accuracy schemes on the two grids produce identical frequencies on an infinite rotating plane, and that, therefore, the two grids are equivalent. Stability analysis of the linearized shallow water equations using leapfrog and semi-implicit time-differencing techniques indicates that viable numerical schemes can be designed on these grids.