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

A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions