Galerkin-type coupled Boundary Element Method for Time domain simulations on Discontinuous surfaces

Abstract

In the context of this abstract, we present the 2D and linearized Galerkin-type coupled BEM (cBEM) that solves for the mixed boundary value problem (BVP) containing the discontinuous free surface and body surface. The incorporation of the high order spectral (HOS) method, introduced by West et al. (1987) and Dommermuth & Yue (1987), allows the monolithic coupling of wave and body dynamics. In the presented application, small amplitude motions of a surface piercing body around its equilibrium position are considered. High-order basis functions are used to approximate the solution function space composed of the velocity potential $\phi$ and its normal derivative $\frac{\partial \phi}{\partial n}$, and the geometry of the body. We discuss the verification of cBEM with an analytic reference solution and demonstrate the validity of the solver for hydrodynamic problems with experimental and numerical data.