强非线性和色散性Boussinesq方程数值模型检验

赵红军; 焦影霞; 孔俊

doi:10.3969/j.issn.0253-4193.2017.05.002

强非线性和色散性Boussinesq方程数值模型检验

doi: 10.3969/j.issn.0253-4193.2017.05.002

河海大学港口海岸与近海工程学院, 江苏南京 210098

基金项目: 江苏省自然科学基金青年基金项目（BK20130827）；交通部重点科技项目（2015328521280）；水利部公益性科研专项（201501010）。

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出版历程
- 收稿日期: 2016-10-14
- 修回日期: 2017-01-15

Numerical validation of a Boussinesq-type model for highly nonlinear and dispersive waves

College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China

摘要

摘要: 采用同位网格有限差分法，建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件，对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算，并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较，从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。
- Boussinesq方程 /
- 非线性 /
- 色散性 /
- 浅水变形
Abstract: In the present work a numerical highly nonlinear and dispersive Boussinesq-type model is developed based on a non-staggered finite difference technique. With the Fourier approximation method providing the incident wave boundary condition, the model is applied and verified against a set of three test cases for which analytical, numerical or experimental reference results are available: (1) propagation of linear and nonlinear periodic waves on deep and shallow depth, (2) shoaling of linear and nonlinear regular waves from deep to shallow water on a mild slope, and (3) transformation of regular waves on a mild slope and on steep slopes. Comparisons of the numerical results with the analytical, numerical and experimental ones confirm the capabilities of the model for the predictions of highly nonlinear and dispersive waves and for the computations of nonlinear wave shoaling on different slopes.
- Boussinesq equation /
- nonlinearity /
- dispersion /
- shoaling

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参考文献(31)

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