Nonlinear fluid-structure interaction of floating bodies

In recent years, free surface flow and fluid-structure interaction problems have received considerable attention from the computational mechanics community. Such problems are particularly difficult because they consist of nonlinear boundary conditions imposed on moving boundaries whose position is part of the problem's solution. The introduction of a rigid body, an additional challenge due to extra integro-differential equations and to possible singularities, has important consequences in the mathematical formulation, but also in the solution algorithm.; In this work, a new comprehensive method has been developed which enables the solution of large, nonlinear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian-Lagrangian approach has been translated into an implicit time integration formulation, a development which enables the use of larger time steps. Novel features of this project include: (1) an implicit formulation 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 formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton-Raphson solver.; The proposed framework has been completed with details on implementation issues. Two types of numerical examples have been used to demonstrate the effectiveness of the method. The first class of examples consists of free surface flows showing finite amplitude waves. The second class of examples deals with large motions of rigid bodies in a fluid with a free surface.