基于半混合欧拉-拉格朗日边界元法不规则波群模拟

doi:10.16183/j.cnki.jsjtu.2023.302

摘要/Abstract

摘要：

为了实现更能表征真实海浪特征的不规则波群的有效模拟,结合不规则波群理论生成方法,开发基于半混合欧拉-拉格朗日边界元方法的数值波浪水池.首先,分析不同模型参数对数值计算的影响.研究发现,波浪模拟精度随阻尼层长度的增加和时间步长的减小而提高,适当的源点外移距离、源点分布范围和源点数量能兼顾计算精度和稳定性.然后,基于验证的模型参数对单向不规则波群进行模拟,将数值模拟结果与物理试验结果和理论目标值进行对比,验证数值水池对不规则波群模拟的有效性.结果表明,所开发的数值水池能有效模拟不规则波群的生成和传播.

关键词: 不规则波群, 数值波浪水池, 半混合欧拉-拉格朗日算法, 边界元法

Abstract:

In order to effectively simulate irregular wave groups that better represent the characteristics of real waves, a numerical wave tank based on a semi-mixed Eulerian-Lagrangian algorithm combined with boundary element method was developed in conjunction with a theoretical generation method for irregular wave groups. First, the impact of model parameters on the numerical solution was analyzed. The results showed that the accuracy of wave simulation improved with an increase in damping layer length or a decrease in the time step. Additionly, selecting appropriate deviation distance, distribution range, and the number of source points can balance computation accuracy and stability. Then, unidirectional irregular wave groups were simulated based on the verified model parameters. The numerical results were compared with the physical test data and theoretical values to validate the performance of the numerical tank in simulating irregular wave groups. The findings indicated that the developed numerical wave tank can effectively simulate the generation and propagation of irregular wave groups.

Key words: irregular wave group, numerical wave tank, semi-mixed Eulerian-Lagrangian algorithm, boundary element method

中图分类号:

U661.1

薛文, 高志亮. 基于半混合欧拉-拉格朗日边界元法不规则波群模拟[J]. 上海交通大学学报, 2025, 59(4): 435-446.

XUE Wen, GAO Zhiliang. Irregular Wave Groups Simulation Based on Semi-Mixed Eulerian-Lagrangian Boundary Element Method[J]. Journal of Shanghai Jiao Tong University, 2025, 59(4): 435-446.

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参数	取值	H_1/3/m			T_1/3/s
参数	取值	目标值	计算值	相对误差/%	目标值	计算值	相对误差/%
L₁	λ₀	0.2	0.197	-1.5	2.22	2.258	1.7
	2λ₀	0.2	0.199	-0.5	2.22	2.253	1.5
	3λ₀	0.2	0.199	-0.5	2.22	2.223	0.1
L₂	λ₀	0.2	0.203	1.5	2.22	2.248	1.2
	2λ₀	0.2	0.201	0.5	2.22	2.224	0.2
	4λ₀	0.2	0.199	-0.5	2.22	2.223	0.1
α₁	2	0.2	0.199	-0.5	2.22	2.214	-0.3
	3	0.2	0.200	0.0	2.22	2.213	-0.4
	4	0.2	0.199	-0.5	2.22	2.223	0.1
	5	0.2	0.200	0.0	2.22	2.205	-0.7
	6	0.2	0.200	0.0	2.22	2.239	0.8
α₂	2	0.2	0.199	-0.5	2.22	2.233	0.6
	3	0.2	0.200	0.0	2.22	2.230	0.4
	4	0.2	0.199	-0.5	2.22	2.223	0.1
	5	0.2	0.201	0.5	2.22	2.210	-0.5
	6	0.2	0.200	0.0	2.22	2.214	-0.3
β	0.1	0.2	0.198	-1.0	2.22	2.228	0.4
	0.2	0.2	0.199	-0.5	2.22	2.235	0.6
	0.3	0.2	0.199	-0.5	2.22	2.223	0.1
	0.4	0.2	0.199	-0.5	2.22	2.233	0.6
	0.5	0.2	0.192	-4.0	2.22	2.249	1.3
l_d	0.5	0.2	0.198	-1.0	2.22	2.252	1.4
	0.6	0.2	0.198	-1.0	2.22	2.241	0.9
	0.7	0.2	0.199	-0.5	2.22	2.243	1.0
	0.8	0.2	0.200	0.0	2.22	2.240	0.9
	0.9	0.2	0.200	0.0	2.22	2.243	1.0
	1.0	0.2	0.199	-0.5	2.22	2.223	0.1
d	λ₀/20	0.2	0.177	-11.5	2.22	2.219	-0.1
	λ₀/10	0.2	0.199	-0.5	2.22	2.223	0.1
	λ₀/5	0.2	0.198	-1.0	2.22	2.222	0.1
n_x×n_z	20×4	0.2	0.199	-0.5	2.22	2.200	-0.9
	20×6	0.2	0.200	0.0	2.22	2.236	0.7
	20×8	0.2	0.199	-0.5	2.22	2.223	0.1
	15×8	0.2	0.191	-4.5	2.22	2.275	2.5
	25×8	0.2	0.204	2.0	2.22	2.193	-1.2
Δt	T₀/100	0.2	0.191	-4.5	2.22	2.036	-8.3
	T₀/150	0.2	0.204	2.0	2.22	2.163	-2.6
	T₀/200	0.2	0.199	-0.5	2.22	2.223	0.1

工况	群性参数	均方根误差/mm	相关系数
1	G_FH=0.6,G_LF=15	8.5	0.77
2	G_FH=0.7,G_LF=15	8.3	0.78
3	G_FH=0.8,G_LF=15	8.0	0.79

工况	H_1/3/mm			T_1/3/s
工况	目标	物理试验	数值计算	目标	物理试验	数值计算
1	70	71 (1.4%)	69 (-1.4%)	1.5	1.562 (4.1%)	1.563 (4.2%)
2	70	79 (12.9%)	65 (-7.1%)	1.5	1.574 (4.9%)	1.514 (0.9%)
3	70	85 (21.4%)	68 (-2.9%)	1.5	1.655 (10.3%)	1.491 (-0.6%)

工况	G_FH			G_LF
工况	目标	物理试验	数值计算	目标	物理试验	数值计算
1	0.6	0.65 (8.3%)	0.64 (6.7%)	15	15.20 (1.3%)	15.87 (5.8%)
2	0.7	0.73 (4.3%)	0.71 (1.4%)	15	15.14 (0.9%)	15.02 (0.1%)
3	0.8	0.81 (1.3%)	0.82 (2.5%)	15	16.60 (10.7%)	14.28 (-4.8%)