  This work discusses the correct modeling of the fully nonlinear free surface
boundary conditions to be prescribed in water waves flow simulations based on
potential flow theory. The main goal of such a discussion is that of
identifying a mathematical formulation and a numerical treatment that can be
used both to carry out transient simulations, and to compute steady solutions
-- for any flow admitting them. In the literature on numerical towing tank in
fact, steady and unsteady fully nonlinear potential flow solvers are
characterized by different mathematical formulations. The kinematic and dynamic
fully nonlinear free surface boundary conditions are discussed, and in
particular it is proven that the kinematic free surface boundary condition,
written in semi-Lagrangian form, can be manipulated to derive an alternative
non penetration boundary condition by all means identical to the one used on
the surface of floating bodies or on the basin bottom. The simplified
mathematical problem obtained is discretized over space and time via Boundary
Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme,
respectively. The results confirm that the solver implemented is able to solve
steady potential flow problems just by eliminating null time derivatives in the
unsteady formulation. Numerical results obtained confirm that the solver
implemented is able to accurately reproduce results of classical steady flow
solvers available in the literature.
