Wave diffraction by floating bodies in water of finite depth using an exact DtN boundary condition

Abstract

For the exact Non-Reflecting Boundary Conditions (NRBCs) or so-called Dirichlet-to-Neumann (DtN) boundary conditions, the artificial boundary is usually chosen as a spherical or ellipsoidal surface by which the computational domain is enclosed fully with finite volume. For the wave diffraction problem in finite-depth water unbounded horizontally, the free water boundary condition and wall boundary condition should be satisfied on still water level (SWL) and seabed, respectively. In this paper, the artificial boundary for DtN condition is chosen as only a lateral cylindrical surface by which it is impossible to envelope the objects and fluid domain fully, but possible by adding still water surface and seabed. A novel DtN condition on the artificial boundary is suggested and then Boundary Element Method (BEM) implementation is described to solve the three-dimensional wave diffraction problems by arbitrary-shaped floating bodies in water of finite depth. Upon successful verification for the case of a bottom-truncated cylinder, the scheme is applied to a single chamfer box and an array of chamfer boxes.