An implicit boundary element solution with consistent linearization for free surface flows and non-linear fluid-structure interaction of floating bodies

In this work, a new comprehensive method has been developed which enables t he solution of large, non-linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian-Lagrangian approach ha s been translated into an implicit time-integration formulation, a developm ent which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formula tion of the rigid-body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulat ion and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such t hat optimal convergence properties are obtained when using a Newton-Raphson solver. The proposed framework has been completed with details on implemen tation issues referring mainly to the computation of the complete initial c onditions and the consistent linearization of the formulation for free surf ace flows. The second part of the paper demonstrates the mathematical and numerical fo rmulation through numerical results simulating large free surface flows and non-linear fluid structure interaction. The implicit formulation using a f ully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surfa ce flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid-structure interacti on examples include the foe and forced motion of a circular cylinder and th e sway, heave and roll motion of a U-shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and perfor mance of the implicit scheme with consistent linearization. Copyright (C) 2 001 John Wiley & Sons. Ltd.