An unconditionally stable scheme for the shallow water equations

A finite-difference scheme for solving the linear shallow water equations i n a bounded domain is described. Its time step is not restricted by a Coura nt-Friedrichs-Levy (CFL) condition. The scheme, known as Israeli-Naik-Cane (INC), is the offspring of semi-Lagrangian (SL) schemes and the Cane-Patton (Cr) algorithm. In common with the latter ii treats the shallow water equa tions implicitly in y and with attention to wave propagation in x. Unlike C P, it uses an SL-like approach to the zonal variations, which allows the sc heme to apply to the full primitive equations. The great advantage, even in problems where quasigcostrophic dynamics are appropriate in the interior, is that the INC scheme accommodates complete boundary conditions.