Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions

The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave-structure interactions. In the present study, the meshless generalized finite difference method (GFDM) together with the second-order Runge-Kutta method (RKM2) is employed to construct a fully three-dimensional (3D) meshless numerical wave flume (NWF). Three numerical examples, i.e., the propagation of freak waves, irregular waves and focused waves, are implemented to verify the accuracy and stability of the developed 3D GFDM model. The results show that the present numerical model possesses good performance in the simulation of nonlinear water waves and suggest that the 3D RKM2-GFDM meshless scheme can be adopted to further simulate more complex nonlinear problems regarding wave-structure interactions in ocean engineering.

Automated summary

The study presents a fully three-dimensional meshless numerical wave flume constructed using the meshless generalized finite difference method (GFDM) and second-order Runge-Kutta method (RKM2). The accuracy and stability of the developed model are verified through numerical examples of freak waves, irregular waves, and focused waves. The results indicate that the model performs well in simulating nonlinear water waves and can be further used to simulate more complex nonlinear problems of wave-structure interactions in ocean engineering.