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, issue 1

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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https://doi.org/10.1155/2013/478054

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:478054

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