An Exact Neumann-to-Dirichlet (NtD) Boundary Condition for Three-Dimensional Wave Motion Over Piecewise Smooth Topographies Near a Vertical Breakwater

Abstract

This paper suggests an exact boundary condition, so-called Neumann-to-Dirichlet (NtD) boundary condition for numerical analysis of the three-dimensional wave motion over piecewise smooth topographies near a vertical breakwater. The semi-infinite water domain in front of the breakwater is converted into a horizontally unlimited water domain by use of the mirror-image method by which the vertical breakwater is neglected and an image of the original undulated seabed is generated. An exact NtD map is derived on a virtual cylindrical surface by which the entire water region is separated into an exterior subregion and an interior subregion involving the original undulated topographies and their imaginary topographies. Based on comparison with the DtN approach from the viewpoint of accuracy, the current model is escalated to consider the effects of heading angle of incident wave and submergence of the shoal at different distance from the breakwater.