  We present an innovative numerical discretization of the equations of
inviscid potential flow for the simulation of three dimensional unsteady and
nonlinear water waves generated by a ship hull advancing in water.
  The equations of motion are written in a semi-Lagrangian framework, and the
resulting integro-differential equations are discretized in space via an
adaptive iso-parametric collocation Boundary Element Method, and in time via
adaptive implicit Backward Differentiation Formulas (BDF) with variable step
and variable order.
  When the velocity of the advancing ship hull is non-negligible, the
semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian
formulation, or ALE) of the free surface equations contains dominant transport
terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG)
method.
  The SUPG stabilization allows automatic and robust adaptation of the spatial
discretization with unstructured quadrilateral grids. Preliminary results are
presented where we compare our numerical model with experimental results on the
case of a Wigley hull advancing in calm water with fixed sink and trim.
