Problems and Improved Methods of 3D Ocean Hydrodynamic Calculation With the σ Coordinate Transformation

BAI Yuchuan; WEN Zhichao; XU Haijue; LIAO Shizhi; CAO Yonggang; XIA Huayong

doi:10.21656/1000-0887.390344

Volume 40 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(8): 840-855

BAI Yuchuan, WEN Zhichao, XU Haijue, LIAO Shizhi, CAO Yonggang, XIA Huayong. Problems and Improved Methods of 3D Ocean Hydrodynamic Calculation With the σ Coordinate Transformation[J]. Applied Mathematics and Mechanics, 2019, 40(8): 840-855. doi: 10.21656/1000-0887.390344

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Problems and Improved Methods of 3D Ocean Hydrodynamic Calculation With the σ Coordinate Transformation

doi: 10.21656/1000-0887.390344

¹State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, P.R.China;²South China Sea Marine Survey and Technology Center, State Oceanic Administration, Guangzhou 510300, P.R.China;³South China Sea Prediction Center, State Oceanic Administration, Guangzhou 510310, P.R.China

Funds: The National Natural Science Foundation of China（41576093）；The National Key R&D Program of China（2018YFC0407505）

Received Date: 2018-12-05
Rev Recd Date: 2019-01-05
Publish Date: 2019-08-01

Abstract

Abstract

The 3D hydrodynamic model plays an important role in accurate simulation of the physical characteristics of the ocean. The complex highorder terms are discarded in the traditional σ coordinate transformation due to the limitation of the computer ability, which causes certain errors or calculation distortions for actual complex terrains (or water depth variations). Therefore, the existent σ coordinate 3D hydrodynamic model was modified in order to meet the needs for highprecision calculation results. In the improved model, the complex highorder terms related to the flow velocity, the water level and the terrain introduced through the σ coordinate transformation were comprehensively considered. The specific interpolation function and the combination of the FEM and the FDM were used to solve the complete 3D shallow water model equations in the σ coordinate system. Compared with the existent model, the improved model has a wider range of applications for changes in the bottom slope, the water depth and the tidal amplitude, which could improve the simulation of the vertical flow distribution characteristics under complex water depth changes and promote the accuracy of the calculation results. The calculation error can be kept in a small range in the improved model under some extreme water conditions (with a tidal amplitude to water depth ratio greater than 0.15), and the improved model can reach a steady state in a short time.
- σ coordinate transformation,
- 3D hydrodynamic model,
- finite element method,
- finite difference method,
- hydrodynamic characteristic

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References(22)

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