Numerical study on the head-on collisions of solitary waves by a harmonic polynomial cell method

Abstract

A 2D fully-nonlinear numerical wave flume is created with a piston-type wave generator based on a recently developed 2D harmonic polynomial cell method (HPC), which has been demonstrated as a highly accurate and efficient approach for modelling of water waves and their interaction with marine structures within the context of potential flow. The overlapping grid technique and a Goring’s wave making method are applied to generate solitary waves. The main focus of this paper is on the head-on collisions of pairwise solitary waves with identical or different amplitudes, including the maximum run-up and spatial phase shift during the whole colliding process. As for collision between identical solitary waves with amplitude σ =0.4, our present numerical results are in excellent agreement with experimental results both in maximum run-up and phase shifts, which indicates the accuracy of HPC method in simulating the head-on collision of solitary waves. The immediate and long-term phase shifts based on wave crest trajectories were obtained with success to explain the inconsistent results of phase shifts between experimental, fully nonlinear numerical results and the third-order approximation results. It is found from the results that the maximum run-up surpasses the sum of the initial wave amplitudes. The analysis of the phase shifts shows that the phase shifts of two solitary waves due to the head-on collision vary with the window length of data and the distance between measurement point and the collision center. The general trend is that the phase shifts measured close to the collision center are larger than those far from the collision center.