A Graphic Processing Unit–High-Order Spectral (GPU-HOS) Numerical Wave Tank for the Simulation of Directional Wave Field Evolution over a Long Time

Abstract

Existing numerical models for direct simulations of stochastically directional waves are limited by their computational burden, and only a few of them can be applied to modeling directional waves on account of nonlinear evolutions on large time scales. In response to these drawbacks, this paper proposes a modified rectangular numerical wave tank based on the high-order spectral (HOS) method. Three main arrangements are responsible for the model improvement. Firstly, the relaxation technique is applied on the four sides of the tank for generating and attenuating waves, with an enhancement in the total computational efforts required of less than 5% being achieved. Secondly, for this paper, the HOS method for solving the nonlinear evolution of waves was modified to a GPU-speedup version for the first time, and the speedup increases dramatically (up to 16-fold) when the grid number is O(106). Thirdly, the higher-order Runge–Kutta method with order 8 is adopted for the purpose of suppressing cumulative temporal errors. Furthermore, several numerical results are presented for the validation of the model. With our modified numerical wave tank, the nonlinear evolutions of random directional waves can be efficiently studied over a large time and space scale.