An Uzawa iterative scheme for the simulation of floating bodies

The numerical simulation of a floating body requires to solve a complex interaction between a free surface flow and the dynamics of the body. In this work we focus on a solution scheme with an explicit representation of the fluid surface and on the specific problem of the imposition of the presence of a floating object. The floating object represents a unilateral constraint on the fluid surface, which cannot rise above the level defined by the floating object itself. We propose a Uzawa type iterative scheme for this type of situation and we describe an efficient implementation in the context of a particular finite element discretization and algebraic splitting procedure.

► The floating problem is rewritten as an inequality-constrained optimization problem.
► The problem is solved with an iterative Uzawa-like methodology.
► Computational costs are reduced through a splitting procedure.
► Further savings result from a particular choice of the finite element discretization.