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

A unified steady and unsteady formulation for hydrodynamic potential flow simulations with fully nonlinear free surface boundary conditions