An unstructured-mesh-based finite element simulation of wave interactions with non-wall-sided bodies

An unstructured-mesh-based finite element method is employed to simulate two-dimensional nonlinear interactions between waves and non-wall-sided floating structures. The velocity potential theory is adopted and the potential is obtained at each time step through solving a matrix equation based on the Galerkin method. The boundary conditions on the free surface are satisfied in the Lagrangian form and the information is updated through the fourth-order Runge–Kutta method. Remeshing based on B-splines is applied regularly to avoid over-distorted elements, and smoothing based on a method using the energy of a curve defined through its nodes is applied to improve the stability of the results. Comparison is made with published results for transient wave motion in a tank to validate the present method. Extensive simulation is made for wedge-shaped bodies in vertical and horizontal motions, and comparison is made with the solution from second-order theory. Results are also provided for wedges in a tank, for wedges in large motion relative to water depth and for twin wedges.