Development and assessment of semi-implicit nonhydrostatic models for surface water waves

Abstract

Abstract This paper presents two semi-implicit nonhydrostatic models to simulate surface water waves. Both models utilize the pressure correction method to solve three-dimensional (3D) incompressible Navier–Stokes equations (NSEs), but one is a noniterative model and the other is associated with iterating to solve the Poisson equation for pressure correction terms. To meet the high computational demands, the Poisson equation is solved on the graphics processing unit (GPU) in conjunction with the conjugate gradient method. Both the accuracy in resolving the linear dispersion relation and the serially implemented efficiency of the models are assessed and discussed. Then, both models are validated with several test cases ranging from shallow to deep water. The results of the two models are very similar and show good agreement with experimental data in the shallow-water test cases. The accuracy of both models are also evaluated in deep-water nonlinear sloshing waves and 2D/3D focusing waves. In addition, the acceleration due to GPU parallelization is evaluated in a final 3D test case.