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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/478054 |
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| author | Guang-an Zou Bo Wang Mu Mu |
| author_facet | Guang-an Zou Bo Wang Mu Mu |
| author_sort | Guang-an Zou |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-183fbde6967a4e30b5906eba83bba558 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-183fbde6967a4e30b5906eba83bba5582025-08-20T03:54:20ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2013/478054 |
| work_keys_str_mv | AT guanganzou stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel AT bowang stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel AT mumu stabilityanalysisofnumericalmethodsfora15layershallowwateroceanmodel |