Evaluation of non-linear wave forces on a fixed body by the higher-order boundary element method

Abstract

A numerical method is developed to evaluate non-linear waves diffracted by a fixed body and the resulting wave force acting on it. The entire boundary and all the variables are discretized by means of isoparametric biquadratic elements. To resolve the difficulty of describing the flow in the intersection region with regular elements, discontinuous elements are introduced. The generalized minimal residual (GMRES) algorithm is implemented to solve the reduced linear algebraic equations. Non-linearity of the free surface is integrated accurately in time by the fourth-order Runge-Kutta method with minimum truncation error. A new numerical radiation condition for non-linear diffraction is suggested, which resolves accurate non-linear diffraction around the body. Non-linear diffraction problem of a bottom-mounted circular cylinder is exemplified. The non-linear wave used by Rienecker and Fenton is chosen as the incident wave field. Based on the numerical results, it is believed that the present method is quite promising.