The quality of simulations in offshore and coastal applications involving waves can be greatly improved with adequate absorbing boundary conditions to prevent spurious reflections. Our particular interest goes out to the simulation of extreme wave impacts on offshore and coastal structures. Impact events are generally short, but since an impact depends on the interaction between different wave systems near the structure, time is required for these systems to develop. During this time, in which waves propagate to and from the structure, we wish to prevent reflections from the outer boundaries of the computational domain. Standard practice has been to extend the domain with dissipation zones. These are straightforward to implement and perform well, provided the dissipation zones are large enough. Unfortunately, the increased domain size takes up computer time and memory, the performance for longer wave components is disappointing and it is not trivial to combine dissipation zones with an incoming wave signal at the boundary. Here we present an alternative. A local generating-absorbing boundary condition for dispersive waves has been developed that renders a boundary transparant to outgoing waves, while waves can enter the domain over the same boundary, at the same time. It is based on Higdon operators, where the phase velocity has been replaced by an approximated dispersion relation, in combination with second derivatives in vertical direction. We will present the derivation of the boundary condition and compare its theoretical performance to the reflection coefficient obtained from numerical simulations. In addition, a comparison between a 3D simulation and experimental results will be discussed.
This is joint work with Mart Borsboom.