This contribution describes a model for the time domain simulation of non linear gravitational water waves past the hull of a boat sailing in calm sea or in regular waves. In non breaking conditions these dispersive waves are marginally affected by viscous dissipation. As such, potential flow theory represents a very competitive alternative to the solution of Navier—Stokes equations. Here, the governing Laplace equation is complemented by non penetration boundary conditions prescribed on the hull surface. The Arbitrary Lagrangian-Eulerian (ALE) form of a similar boundary condition is also imposed on the water free surface to close the fluid problem, while an additional dynamic free surface boundary condition in ALE form is imposed to compute the evolution of the free surface shape. The mathematical problem obtained is discretized over space via a Boundary Element Method (BEM) implemented in the open source C++ library π-BEM, while an Implicit Backward Difference Formula (BDF) scheme of arbitrary order and step size is used for the space discretization. The dominant transport terms appearing in the dynamic free surface boundary condition are stabilized via Streamwise Upwind Petrov—Galerkin (SUPG) scheme. The solver is directly implemented with CAD data structures, to allow for the hull computational grid to be continuously deformed sliding on the hull surface, as its free surface boundary is deformed by the forming and passing waves. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.