Nonlinear perturbations on a free surface induced by a submerged body: A boundary integral approach

The Boundary Integral scheme developed by Dold and Peregrine¹ has been extended and modified in order to allow for the investigation of non-periodic (spatial) disturbances on a free surface of water produced by a submerged body. The problem is treated as two dimensional: the body is shaped like a horizontal long cylinder with an arbitrary smooth contour, (a twice differentiable closed curve), moving in a direction perpendicular to its generators; the cylinder can execute any twice differentiable, (with respect to time), prescribed motion. The numerical code has been successfully implemented and produces accurate results with a comparatively small computational effort. The method has several features which enhance efficiency and precision. Among these: there is an economical high order discretization of the system of integral equations; the resulting system of linear algebraic equations is solved by a Gauss-Seidel iterative scheme which converges in few iterations, less than 10 usually; a fifth order Taylor series is used to march in time. Numerical results are presented; for a weir set in an otherwise uniform current, radiation of waves produced by simple oscillatory movements of a cylinder, and the interaction of an incoming solitary wave with a fixed submerged cylinder are shown.