Numerical analysis on the generation, propagation and interaction of solitary waves by a Harmonic Polynomial Cell Method

A numerical wave tank based on the Harmonic Polynomial Cell (HPC) method is created to study the generation, propagation and interaction of solitary waves. The HPC method has been proven to be of high accuracy and efficiency in modeling of water waves, wave–wave and wave–structure interaction within...

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Bibliographic Details
Published in:Wave motion 2019-05, Vol.88, p.34-56
Main Authors: Tong, Chao, Shao, Yanlin, Hanssen, Finn-Christian W., Li, Ye, Xie, Bin, Lin, Zhiliang
Format: Article
Language:English
Subjects:
Cartesian coordinates
Estimating techniques
Fluid mechanics
Free surfaces
Harmonic Polynomial Cell Method
Mathematical analysis
Mathematical models
Model accuracy
Numerical analysis
Overtaking
Polynomials
Potential flow
Solitary wave
Solitary waves
Surface waves
Water depth
Water waves
Wave generation
Wave interaction
Wave propagation
Wave tanks
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Summary:A numerical wave tank based on the Harmonic Polynomial Cell (HPC) method is created to study the generation, propagation and interaction of solitary waves. The HPC method has been proven to be of high accuracy and efficiency in modeling of water waves, wave–wave and wave–structure interaction within the context of potential flow. An important feature of the present HPC method is that the free surface and solid boundaries are immersed in a stationary Cartesian grid. Solitary waves with σ, i.e. amplitude to water depth ratio, up to 0.6 are generated by different methods. We demonstrate that the results based on the first-, third- and ninth-order method are less satisfactory than the fully-nonlinear method in generating solitary waves withσ>0.4. Additionally, both the head-on and overtaking collision between two solitary waves are studied. In the investigation of the phase shifts after the head-on collision, our window model successfully explain the main reason why Su and Mirie (1980)’s third-order approximation of the uniform phase shifts is inconsistent with Chen and Yeh (2014)’s experimental results and Craig et al. (2006)’s fully nonlinear numerical results. For the overtaking collision of solitary waves, the collision process and the phase shifts are numerically analyzed. Our present result also confirms Craig et al. (2006)’s category of the overtaking collision.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2019.01.007