Stability of a FBTCS Scheme Applied to the Propagation of Shallow-Water Inertia-Gravity Waves on Various Space Grids

The equations governing the propagation of inertia-gravity waves in geophysical fluid flows are discretized on the A, B, C, and D grids according to the classical forward-backward on time and centered on space (FBTCS) numerical scheme. The von Neumann stability analysis is performed and it is shown that the stability condition of the inertia-gravity waves scheme is more restrictive, at least by a factor of , than that concerning pure gravity waves, whatever the magnitude of the Coriolis parameter. Finally, the general necessary and sufficient stability condition is derived for the A, B and C grids, while, on the D grid, the stability condition has been obtained only in particular cases.