Improvement in the SPH-Paddle Wave Maker Approach for Real Tsunami Waves Modeling

The present study focused on generation of representative waves of tsunamis using GPU-based SPH numerical method. In this regard, solitary waves, as traditional representative of leading waves of tsunamis, were firstly generated in SPH model by a piston wave-maker moving based on an implicit equation solved by numerical code. Since it was proved that solitary waves are remarkably shorter and steeper than real-world tsunami waves, a new approach was also presented to reproduce the very long wave of a real tsunami. In this method, the tsunami time series was approximated by a theoretical relation based on the combination of several solitons. The relation was then used to solve the linearized trajectory equation of a wave-maker for generation of the intended time series of tsunami wave in the SPH model. The generation of solitary wave in SPH model was evaluated by comparing different simulated waves with analytical ones and it was seen that the solitary waves are successfully generated. In order to consider the accuracy of SPH formulation for simulation of the solitary wave evolution, an experimental case of breaking solitary wave propagation over a composite beach was also simulated. Although numerical results demonstrated a slight spurious wave-height decay, the SPH model satisfactorily reproduced the entire evolution phases of the solitary wave including wave propagation over a flat bottom, wave shoaling on a slope and wave breaking. For verification of the proposed approach in reproduction of real-world tsunami measurements, the time series of surface elevation record of the 2004 Indian Ocean tsunami was generated in SPH model. The results demonstrated that the tsunami record is successfully generated using the piston wave-maker. Thus, the presented approach can be regarded as a suitable method for representing the very long wave of the tsunami instead of the traditional options.