Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model

Guang-an Zou, Bo Wang and Mu Mu

Journal of Applied Mathematics, 2013, vol. 2013, 1-12

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:478054

DOI: 10.1155/2013/478054

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