An innovative open boundary treatment for nonlinear water waves in a numerical wave tank
Problems defined on infinite domains must be treated on a finite computational domain. The treatment of the artificially placed boundaries (usually referred to as open boundaries) of such domain truncations can be quite subtle; an over truncation would normally result in large, undesirable reflection of signals back to the computational domain whereas an under truncation would imply an injudicious use of computational resources. In particular, problems occur when strongly nonlinear free surface waves generated in a numerical wave tank are passing through such an open boundary.\newline In this paper, some recent numerical test results of an innovative treatment of open boundaries are presented. One of popularly adopted techniques of minimizing wave reflections at open boundaries is to use an ``absorbing beach", over which wave energy is dissipated. In addition to a kinetic energy based dissipation term traditionally added to the dynamical boundary condition to form an ``absorbing beach", a potential energy based term is added, tested and compared with the case of kinetic energy dissipation alone. Our numerical results show that the newly added dissipation mechanism can dissipate energy more effectively over an absorbing beach and consequently result in a much less reflection of wave energy back to the computational domain.
Zhu, S. (2001). An innovative open boundary treatment for nonlinear water waves in a numerical wave tank. Computer Modeling in Engineering and Sciences, 2 (2), 227-236.