Three-dimensional numerical simulation of solitary wave run-up using the IB 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. © 2013 Elsevier B.V.