Stability analysis of numerical methods for a 1.5-layer shallow-water ocean model

A 1.5-layer reduced-gravity shallow-water ocean model in spherical coordinates is described and discretized in a staggered grid (standard arakawa c-grid) with the forward-time central-space (ftcs) method and the leap-frog finite difference scheme. the discrete fourier analysis method combined with the gershgorin circle theorem is used to study the stability of these two finite difference numerical models. a series of necessary conditions of selection criteria for the time-space step sizes and model parameters are obtained. it is showed that these stability conditions are more accurate than the courant-friedrichs-lewy (cfl) condition and other two criterions (blumberg and mellor,1987; casulli,1990,1992). numerical experiments are proposed to test our stability results,and numerical model that is designed is also used to simulate the ocean current. © 2013 guang-an zou et al.