A High-order Spectral Method for Simulation of Nonlinear Wave Generation due to Bottom Movement

In this study, we presented a high-order spectral method capable of simulating the generation of nonlinear waves due to bottom movement. The governing equations were based on dynamic and kinematic free surface boundary conditions, and the nonlinear terms of each boundary condition were calculated in physical space using a pseudo-spectral method, then redefined in Fourier space. The time integration of the governing equations was analyzed using the fourth-order Runge-Kutta method. The computed velocity potential was redefined at the mean water level through Taylor series expansion, which always satisfies the continuity equation and kinematic bottom boundary condition. Fast Fourier Transform was used for calculations in both physical and Fourier spaces. To verify the model's accuracy, we compared it with existing experimental results, which showed a closer match to experimental data than the linear results. When applying maximum perturbation order (M) of 3 or more, the results converged closely.