Higher-order boundary element simulation of fully nonlinear wave radiation by oscillating vertical cylinders

The application of a higher-order boundary element method in the numerical simulation of nonlinear waves radiated by a forced oscillating vertical circular cylinder is described. In this time-domain approach, the higher-order boundary element method is used to solve the mixed boundary value problem based on an Eulerian description at each time step. The 4th-order Runge–Kutta scheme is adopted to update the free water surface boundary conditions expressed in a Lagrangian formulation. For the calculation of hydrodynamic forces, some auxiliary functions are used instead of predicting the time derivative of the potential directly. In order to avoid wave reflection from the far-field boundary, an artificial damping layer is distributed on the outer part of the free surface. On the surfaces of the domain, the computational meshes are composed of unstructured triangular elements on the free surface, and quadrilateral elements elsewhere. Additionally, mesh regridding using the Laplace smoothing technique and interpolation are applied on the free surface to deal with possible numerical instability. Numerical results are obtained for a series of wave radiation problems, as well as for the interaction of an impulse wave with a circular cylinder in a circular tank.