A numerical approach to three-dimensional diffraction problem in non-linear waves

In the present study, non-linear diffraction waves around a body are considered due to non-linear incident waves. The non-linear waves approach the body from infinity. In order to realize it numerically, a new approach is tried with a reasonable radiation condition. All the boundaries and variables are discretized by means of isoparametric bi-quadratic elements, but discontinuous elements are used around intersections and corners. Influence coefficients are effectively calculated by the Gauss-Legendre quadrature and the triangle polar coordinate mapping. The GMRES(Generalized Minimal RESidual) algorithm is adopted to solve the resulting linear algebraic systems. Non-linearity of the free surface is accurately integrated in time by using the fourth-order Runge-Kutta method with minimum truncation error. As a numerical example, the non-linear diffraction of a bottom-mounted circular cylinder is considered. The non-linear waves by Rienecker & Fenton are chosen as incident waves. Computed non-linear diffraction waves and forces seem quite reasonable. Further study is required to validate the present method.