Simulation of three-dimensional nonlinear water waves using a pseudospectral volumetric method with an artificial boundary condition

This article presents a pseudospectral method for the simulation of nonlinear water waves described by potential flow theory in three spatial dimensions. The method utilizes an artificial boundary condition that limits the vertical extent of the fluid domain, and it is found that the reduction in domain size offered by the boundary condition enables the solution of the Laplace problem with roughly half the degrees of freedom compared to another spectral method in the literature for (wave number times water depth) kh >= 2 pi. Moreover, it is found that the location of the artificial boundary condition can be chosen once and for all at the beginning of simulations such that the size of the fluid domain is reduced substantially, even when the lowest point of the free surface elevation varies significantly with time. The method is tested by simulating steady nonlinear wave trains, the development of crescent waves from a steady nonlinear wave train, a nonlinear focusing event, and a Gaussian hump which is initially at rest. It is shown that in all, but the most nonlinear cases, the method is capable of obtaining accurate results.