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

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  • Guang-an Zou
  • Bo Wang
  • Mu Mu

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.

Suggested Citation

  • Guang-an Zou & Bo Wang & Mu Mu, 2013. "Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-12, November.
    • Handle: RePEc:hin:jnljam:478054
    DOI: 10.1155/2013/478054
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