四叉树网格下的椭圆型缓坡方程数值模型研究

唐军; 李巧生; 沈永明

doi:10.3969/j.issn.0253-4193.2013.05.018

四叉树网格下的椭圆型缓坡方程数值模型研究

doi: 10.3969/j.issn.0253-4193.2013.05.018

1.
大连理工大学海岸和近海工程国家重点实验室, 辽宁大连 116023
2.
大连理工大学海岸和近海工程国家重点实验室, 辽宁大连 116023;江苏省苏州市航道管理处, 江苏苏州 215008

基金项目: 国家重点基础研究发展计划项目(2013CB430403)和国家自然科学基金项目(51279023;50709004)。

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出版历程
- 收稿日期: 2012-10-25

Numerical study of the elliptic mild-slope equation for water wave in quadtree grid system

1.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China
2.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China;Suzhou Waterways Management Division, Suzhou 215008, China

摘要

摘要: 波浪是近岸海域关键的水动力因素之一。考虑到近岸地形复杂、波浪演化显著的特点,建立了四叉树网格体系下的椭圆型缓坡方程数值模型,采用有限体积法对模型进行数值离散,应用GPBiCG(m, n)算法求解离散后的控制方程。模型中根据波浪波长布局计算网格,生成多层次四叉树网格,对复杂计算域有较好的适应性,并且在离散和方程求解中无需引入形函数、不产生复杂的交叉项,节约了存储空间和计算时间。将模型成功应用于物理模型实验及Acapulco海湾的波浪场数值模拟,结果表明该模型能够准确、高效地模拟近岸波浪场,可为近岸波浪场的模拟提供一定的理论和技术支持。
- 波浪 /
- 椭圆型缓坡方程 /
- 四叉树网格 /
- 有限体积法
Abstract: Water wave is important hydrodynamics in coastal zone. As the evolution of water wave in the coastal zone is complex due to complex topography, a numerical model of elliptic mild-slope equation was developed in quadtree grid system. The numerical model was discretized by finite volume method and solved by GPBiCG(m,n)algorithm.The numerical model has good adaptability with the complex topography as it can generate multi-level quadtree grids in accordance with the water wave length.Compared with other numerical scheme, this model does not introduce shape function and complex cross-term, and is efficient in storage and computation. The numerical model was used to simulate the water wave propagation in experiment and the Acapulco Bay. The numerical results show that this model is accurate and efficient in simulating coastal water waves.It is believed that this model can be an effective tool for coastal water wave simulation in engineering or study.
- water wave /
- elliptic mild-slope equation /
- quadtree grid /
- finite volume method

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