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

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 t...

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Main Authors: Guang-an Zou, Bo Wang, Mu Mu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/478054
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spelling doaj-183fbde6967a4e30b5906eba83bba5582020-11-24T21:42:05ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/478054478054Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean ModelGuang-an Zou0Bo Wang1Mu Mu2Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, ChinaInstitute of Applied Mathematics, Henan University, Kaifeng 475004, ChinaKey Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, ChinaA 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.http://dx.doi.org/10.1155/2013/478054
collection DOAJ
language English
format Article
sources DOAJ
author Guang-an Zou
Bo Wang
Mu Mu
spellingShingle Guang-an Zou
Bo Wang
Mu Mu
Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
Journal of Applied Mathematics
author_facet Guang-an Zou
Bo Wang
Mu Mu
author_sort Guang-an Zou
title Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
title_short Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
title_full Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
title_fullStr Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
title_full_unstemmed Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
title_sort stability analysis of numerical methods for a 1.5-layer shallow-water ocean model
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/478054
work_keys_str_mv AT guanganzou stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel
AT bowang stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel
AT mumu stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel
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