Using a local radial basis function collocation method to approximate radiation boundary conditions

The local radial-basis-function collocation method (LRBFCM) based on the multiquadric type radial basis function is used to simulate the water wave propagation with oblique incidence and radiation. In this study, the mild-slope equation is applied and the radiation boundary condition is expanded to the third-order approximation. Two numerical cases are considered for verification, which include wave scattering around a vertical cylinder and shallow water wave passed over a submerged shoal. Numerical results based on the third-order radiation boundary condition are found to be in a better agreement than those of the first-order and second-order radiation boundary conditions especially for large incidence or radiation angles. Overall, the LRBFCM is a meshless numerical method and its applications to the high-order radiation boundary condition are much simpler compared with the traditional numerical methods, such as the finite difference method and the finite element method.