Second order wave diffraction around two-dimensional bodies by time-domain method

Abstract

A time-domain second order method is developed to study the nonlinear wave forces and runupon a surface piercing body of arbitrary shape in two dimensions. The free surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time and the field solution at each time step is obtained by an integral equation method based on Green's theorem. The solution is separated into a known incident potential and a scattered potential. The initial condition corresponds to a Stokes second order wave field in the domain, and the scattered potential is allowed to develop in time and space. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. Comparisons of wave forces are made with previous theoretical and experimental results for the case of a semi-circular cylinder with axis at the still water level and a favourable agreement is indicated.