Numerical simulation of the dynamics of boats by a variational inequality approach

In this chapter we present some recent numerical studies on fluid–structure interaction problems in the presence of free surface flow. We consider the dynamics of a rowing boat, simulated as a rigid body. We focus on an approach based on formulating the floating body problem as an inequality constraint on the water elevation. A splitting procedure is used to develop an efficient numerical scheme where the inequality constraint is imposed only on a wave-like equation representing an hydrostatic approximation of the hydrodynamic equations. Numerical tests demostrate the effectiveness of the proposed procedure.