Nonlinear wave-structure interactions with a high-order Boussinesq model

This paper describes the extension of a finite difference model based on a recently derived highly accurate Boussinesq formulation to include domains having arbitrary piecewise-rectangular bottom-mounted (surface-piercing) structures. The resulting linearized system is analyzed for stability on a structurally divided domain, and it is shown that exterior corner points pose potential stability problems, as well as other numerical difficulties. These are mainly due to the discretization of high-order mixed-derivative terms near these points, where the flow is theoretically singular. Fortunately, the system is receptive to dissipation, and these problems can be overcome in practice using high-order filtering techniques. The resulting model is verified through numerical simulations involving classical linear wave diffraction around a semi-infinite breakwater, linear and nonlinear gap diffraction, and highly nonlinear deep water wave run-up on a vertical plate. These cases demonstrate the applicability of the model over a wide range of water depth and nonlinearity.