A Nested Domains Technique for a Fully Nonlinear Unsteady Three-Dimensional Boundary Element Method for Free-Surface Flows with Forward Speed

This paper presents the work on a fully nonlinear body-exact unsteady three-dimensional boundary element method (BEM) for free-surface flows with forward speed based on potential flow theory. The BEM is coupled with free-surface markers updated in a semi-Lagrangian way. Time-dependent nonlinear boundary conditions are applied on the instantaneous position of the free-surface and the wetted surface of the body and the boundary value problem (BVP) is solved at each time step in an earth-fixed reference frame, thus using a moving grid technique. A fourth-order Runge-Kutta scheme is used for the time-integration of the free-surface boundary conditions controlling the free-surface markers. The ongoing development of this method is done with the outlook of computing ship motions although this paper only discusses captive hull computations with forward speed in calm water for the purpose of validating the forward speed effects in a controlled manner, thus keeping the same mathematical model and approach developed for the wave-body interaction.