Three-dimensional numerical simulation of solitary wave run-up using the lB method

Abstract

Although the finite difference method is computationally efficient, it is acknowledged to be inferior when dealing with flow-over on structures with a complex geometry because of its rectilinear grid system. Therefore, we developed a numerical procedure that can cope with flow over structures with complex shapes while, at the same time, retaining the simplicity and efficiency of a rectilinear grid system. We used the immersed boundary method, which involves application of immersed boundary forces at solid boundaries rather than conventional boundary-conditions, to-investigate-wave-interactions with-coastal-structures-in a-three-dimensional numerical wave tank by solving the Navier Stokes equations for two-phase flows. We simulated the run-up of a solitary wave around a circular island. Maximum run-up heights were computed around the island and compared with available laboratory measurements and previous numerical results. The three-dimensional features of the run-up process were analyzed in detail and compared with those of depth-integrated equations models.