Study On Nonlinear Numerical Water Wave Tank By A Harmonic Polynomial Cell Method

Numerical water wave tank plays a significant role in simulating water waves and study on wave-wave and wave-structure interaction.We created a 2D numerical water wave tank based on a Harmonic Polynomial Cell method,which is of high accuracy and efficiency in solving Laplace equation.This wave tank is capable of generating waves by both the Velocity Inlet Wave Making method and the Wave-maker Imitating method.The Immersed Boundary method is applied in dealing with the free surface,and we set a moving overlapping wave-maker grid on the background grid to increase the accuracy of simulation of free surface.To test the performance of this numerical wave tank,we firstly simulated solitary waves in shallow water,including the generation,propagation and interaction of solitary waves.1)Imposing fully nonlinear solitary wave solution on the wave making boundary,we used Velocity Inlet Wave Making method to generate ‘pure' solitary waves,whose amplitudes could reach the expected values and which could propagate steadily with more negligible trailing waves.2)As for the head-on collision of two solitary waves,the maximum run-up is higher than linear superposition of two initial amplitudes and this phenomenon becomes more obvious with the increase of nonlinearity of solitary waves.We validated our numerical results of maximum run-up,phase shifts,and trailing waves after symmetric head-on collision for solitary waves with amplitudes ?=0.4.The comparison with experimental results confirmed the correctness of our numerical calculations so that we set extra four different cases including symmetric and asymmetric collisions based on the validation.3)Many researchers had noticed that their experimental and numerical results differed a lot from the third-order theoretical solution about phase shifts after head-on collision.With respect to this question,we set up a measuring model to successfully give the main reason.4)As for the overtaking collision of solitary waves,we validated the category of previous researchers based on wave profile and ratio of amplitudes of two solitary waves and got the phase shifts after interaction for different types of overtaking collisions.After confirming the rightness of our numerical wave tank in simulating shallow water waves,we also simulated rogue waves in finite and deep water.We used three different mechanisms to generate rogue waves,including wave energy focusing at specific position and time,modulational instability and by three trains of random waves.1)As for the simulation of focusing waves,we found that our numerical results were consistent with linear analytical results when the wave slopes were set small.However,with the increase of nonlinearity of waves,the difference between numerical and analytical results was getting more obvious closer to focal position.2)The same as focusing wave,we also found that our numerical simulation of rogue waves by modulational instability was in agreement with the linear analytical results when the wave nonlinearity were small.The difference between numerical and analytical results became obvious with the increase of frequency bandwidth and wave slope.3)With respect to generating rogue waves by random waves,we adopted the superposition of three wave trains based on water wave energy spectrum.These three trains of random waves possess different percentages of energy so that we can simulate real random waves on ocean while generating rogue waves at a designed position and moment.We also found that our numerical wave profiles were in consistent with linear solutions away from focal position,but the linear analytical solutions could not predict the wave profile and wave height in focal domain.