An hybrid boundary element method for free surface flows

A hybrid Boundary Element Method to solve the Laplace equation is presented. The method solves the Boundary Integral Equation coming from the Laplace equation. Both Neumann and Dirichlet boundary conditions are presented. The Neumann boundary conditions are implemented also in a weak formulation. This formulation is inserted into the algebraic system of the hybrid BEM in an innovative way. We present the convergence analysis of the method applied to three known reference solution. Then the hybrid BEM is modified in order to treat free surface flow, namely the case of a body in motion in water. Both a submerged body and a surface piercing body are considered. Linearized free surface boundary conditions are implemented. A Streamline Upwind Petrov Galerkin stabilization is used to implemented the linearized free surface condition. This allows us to use non conformal unstructured grids.