适于模拟不规则水域波浪的缓坡方程两种数值模型比较

李巧生; 唐军; 吕义港

doi:10.3969/j.issn.0253-4193.2020.01.004

适于模拟不规则水域波浪的缓坡方程两种数值模型比较

doi: 10.3969/j.issn.0253-4193.2020.01.004

1.
苏州市航道管理处，江苏苏州 215008
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
3.
嘉兴市交通工程质量安全管理服务中心，浙江嘉兴 314001

基金项目: 国家重点研发计划（2017YFC1404200）；国家自然科学基金（51579036）；中央高校基本科研业务费（DUT19LAB13）。

详细信息

作者简介:
李巧生（1985—），男，江苏省盐城市人，从事港口与航道整治工程及近岸水动力研究。E-mail：LQS20056789@163.com

中图分类号: P731.22
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- 被引次数: 0
出版历程
- 收稿日期: 2018-11-14
- 修回日期: 2018-12-21
- 网络出版日期: 2021-04-21
- 刊出日期: 2020-01-25

Comparisons of the two numerical models of elliptic mild-slope equation for wave propagation in irregular coastal zones

1.
Suzhou Waterway Administration Office, Suzhou 215008, China
2.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China
3.
Jiaxing City Traffic Engineering Quality and Safety Management Service Center, Jiaxing 314001, China

摘要

摘要: 本文分析比较了适于不规则水域波浪模拟的椭圆型缓坡方程两种数值模型。两种数值模型均采用有限体积法离散，分别基于四叉树网格和非结构化三角形网格建立。首先结合近岸缓坡地形上波浪传播的经典物理模型实验对两种数值模型分别进行了验证，并结合计算结果对比分析了两种模型的计算精度和效率。计算结果表明，两种数值模型均可有效地模拟近岸波浪的传播变形；相对非结构化三角形网格下的模型，基于四叉树网格建立的数值模型在数值离散和求解过程中无需引入形函数、不产生复杂的交叉项，离散简单，易于程序实现，且节约计算存储空间，计算效率高。
- 波浪 /
- 数值模拟 /
- 椭圆型缓坡方程 /
- 四叉树网格 /
- 非结构化网格
Abstract: In this paper, two numerical models of elliptic mild-slope equation for coastal wave propagation in coastal zones are compared and analyzed. The two numerical models are developed by using finite volume method respectively on adaptive quadtree mesh and triangular unstructured mesh. The numerical models are firstly used to simulate wave propagation and deformation on circle and elliptic shores, and the computational efficiencies are compared and analyzed based on the numerical results. The numerical results show that both of the two numerical models are effective in simulating coastal wave propagation and deformation. Compared with the numerical model on unstructured triangular mesh, the numerical model on quadtree mesh is more concise and easy for numerical implementation as it does not involve complex cross-terms due to model transformation in the process of numerical discretization. What’s more, the numerical model on quadtree mesh is more efficiency in saving computing time and storage space.
- wave /
- numerical simulation /
- elliptic mild-slope equation /
- quadtree grid /
- unstructured grid

HTML全文

图 1 四叉树网格不同分级单元间的通量计算

Fig. 1 Flux across different graded cell interfaces

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图 2 格林函数法计算示意图

Fig. 2 Diagram of Green function method

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图 3 圆形浅滩计算域地形示意图

Fig. 3 Topography of a circular shoal zone

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图 4 圆形浅滩计算域网格图

a. 自适应四叉树网格图；b. Delaunay三角化网格图

Fig. 4 Numerical grids of a circular shoal zone

a. Adaptive quadtree grid graph; b. Delaunay triangulated grid graph

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图 5 圆形浅滩数值模拟相对波高等值线图

a. 自适应四叉树模拟的相对波高；b. Delaunay三角化模拟相对波高

Fig. 5 Contours of simulated wave height for wave propagation on a circular shoal

a. Relative wave height of adaptive quadtree simulation; b. relative wave height of Delaunay triangulated simulation

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图 6 圆形浅滩地形上波高数值解与实测值^[16]的比较

Fig. 6 Comparison between numerical simulated and measured^[16] wave heights on a circular shoal

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图 7 椭圆形浅滩计算域地形

Fig. 7 Topography of a elliptic shoal zone

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图 8 椭圆形浅滩计算域网格图

a. 自适应四叉树网格图；b. Delaunay三角化网格图

Fig. 8 Numerical grids of an elliptic shoal zone

a. Adaptive quadtree grid graph; b. Delaunay triangulated grid graph

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图 9 椭圆形浅滩数值模拟相对波高等值线图

a. 自适应四叉树模拟的相对波高图；b. Delaunay三角化模拟相对波高图

Fig. 9 Contours of simulated wave height for wave propagation on an elliptic shoal

a. Relative wave height of adaptive quadtree simulation; b. relative wave height of Delaunay triangulated simulation

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图 10 椭圆形浅滩地形上波高数值解与实测值^[17]的比较

Fig. 10 Comparison between numerical simulated and measured ^[17] wave heights on an elliptic shoal

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表 1 圆形浅滩地形上两种计算网格下的模型效率比较

Tab. 1 Comparison of the efficiency for the model in two kind of numerical grids on a circular shoal

	网格个数	网格步长/m	迭代步数	计算时间/s	计算精度
自适应网格下的模型	7 288	0.025×0.018 75， 0.05×0.037 5	445	4.906	1.0×10⁻⁷
Delaunay三角化网下的模型	8 278	0.03	630	6.51	1.0×10⁻⁷

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表 2 椭圆形浅滩地形上两种计算网格下的模型效率比较

Tab. 2 Comparison of the efficiency for the model in two kind of numerical grids on an elliptic shoal

	网格个数	网格步长/m	迭代步数	计算时间/s	计算精度
自适应网格下的模型	11 308	0.335 937 5×0.312 5， 0.167 968 75×0.156 25， 0.083 984 375×0.078 125	445	97.109	1.0×10⁻⁷
非结构化网格下的模型	30 618	0.12	630	151.14	1.0×10⁻⁷

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