Higher-order Spectral Method for Regular and Irregular Wave Simulations

Abstract

In this study, a nonlinear wave simulation code is developed using a higher-order spectral (HOS) method. The HOS method is very efficient because it can determine the solution of the boundary value problem using fast Fourier transform (FFT) without matrix operation. Based on the HOS order, the vertical velocity of the free surface boundary was estimated and applied to the nonlinear free surface boundary condition. Time integration was carried out using the fourth order Runge–Kutta method, which is known to be stable for nonlinear free-surface problems. Numerical stability against the aliasing effect was guaranteed by using the zero-padding method. In addition to simulating the initial wave field distribution, a nonlinear adjusted region for wave generation and a damping region for wave absorption were introduced for wave generation simulation. To validate the developed simulation code, the adjusted simulation was carried out and its results were compared to the eighth order Stokes theory. Long-time simulations were carried out on the irregular wave field distribution, and nonlinear wave propagation characteristics were observed from the results of the simulations. Nonlinear adjusted and damping regions were introduced to implement a numerical wave tank that successfully generated nonlinear regular waves. According to the variation in the mean wave steepness, irregular wave simulations were carried out in the numerical wave tank. The simulation results indicated an increase in the nonlinear interaction between the wave components, which was numerically verified as the mean wave steepness. The results of this study demonstrate that the HOS method is an accurate and efficient method for predicting the nonlinear interaction between waves, which increases with wave steepness.