Second-Order Radiation Boundary Condition for Water Wave Simulation with Large Angle Incidence

A finite-element method (FEM) is used to simulate water wave propagation with large angle incidence at exterior boundaries. In this paper, the radiation boundary condition is expanded to a second-order approximation and a quadratic shape function is used in the FEM wave model. Cases used for verifications include wave scattering around a vertical cylinder and wave propagation over a submerged circular shoal with concentric contours. Numerical calculations based on this second-order radiation boundary condition are found to be in good agreement with theoretical and experimental results available. The numerical predictions show that this model has made a very good improvement over the first-order radiation boundary conditions for oblique wave incidence in coastal engineering.