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Journal of Applied Mathematics
Volume 2013, Article ID 478054, 12 pages
Research Article

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

1Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Institute of Applied Mathematics, Henan University, Kaifeng 475004, China

Received 7 March 2013; Accepted 12 September 2013

Academic Editor: Jong Hae Kim

Copyright © 2013 Guang-an Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.