A multi-layer Boussinesq-type model with second-order spatial derivatives:Theoretical analysis and numerical implementation
A multi-layer Boussinesq-type model with second-order spatial derivatives:Theoretical analysis and numerical implementation
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具有二阶空间导数的多层Boussinesq型模型：理论分析与数值实现
DOI：
10.1016/j.oceaneng.2019.106545
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发表时间：
2019
影响因子：
5
通讯作者：
Jiawen Sun
中科院分区：
文献类型：
--
作者：
Zhongbo Liu;Kezhao Fang;Jiawen Sun
本文从理论和数值上研究了Liu et al.（2018）提出的最高空间导数为2的多层Boussinesq型模型中体现的线性和非线性特性的准确性。理论分析表明，四层模式精度最高，在1%的误差范围内，相坐标tokh= 179.3（其中k为波数，k为典型水深），线速度分量kh= 69.7，线性变浅幅度kh = 141.8。在相同的容差误差下，超谐波和次谐波传递函数分别精确到tokh= 138.5和80，三阶谐波和振幅色散精确到tokh= 127.2。线速度分布也达到了很高的精度，对于两层、三层和四层模型，分别为kh = 4.5、14.9和69.7。采用时间积分的复合四阶Adams-Bashforth-莫尔顿格式建立了垂向二维数值模式。数值模拟了规则波在缓坡上的线性变浅、规则波在潜堤上的非线性演化和定水深下的聚焦波群演化。计算结果与实验数据吻合较好。进一步比较了n = 2和n = 3两层模型的计算时间，结果表明n = 2两层模型的计算效率提高了约1/3。
The accuracy of the linear and nonlinear properties embodied in multi-layer Boussinesq-type models with the highest spatial derivativenbeing 2, as proposed by Liu et al. (2018), is theoretically and numerically investigated in this paper. Theoretical analysis shows that the four-layer model has the highest accuracy and is applicable up tokh= 179.3 (wherekis the wavenumber, andhis a typical water depth) in phase celerity at a 1% tolerance error,kh= 69.7 in the linear velocity components andkh= 141.8 in linear shoaling amplitude. At the same tolerance error, the super- and sub-harmonic transfer functions are accurate up tokh= 138.5 and 80, respectively, and the third-order harmonics and amplitude dispersion are accurate up tokh= 127.2. A high accuracy of the linear velocity profiles is also achieved and is approximatelykh= 4.5, 14.9 and 69.7 for the two-layer, three-layer and four-layer models, respectively. Vertical two dimensional (2D) numerical models are established with a composite fourth-order Adams-Bashforth-Moulton scheme in time integration. Numerical simulations, including linear shoaling of regular waves over a mild slope, nonlinear regular wave evolution over a submerged breakwater and focusing wave group evolution over a constant water depth, are carried out. The computed results are in reasonable agreement with the experimental data. Furthermore, the CPU times for the two-layer model withn= 2 and the two-layer model withn= 3 are compared, and the numerical efficiency of the two-layer model withn= 2 increases by approximately 1/3.