Abstract : In this short course we are going to review some of the main existing Eulerian approaches to the numerical simulation of the full water wave problem. More specifically, the lectures willl cover the boundary integral equation method, higher order spectral method, Dirichlet-to-Neumann operator approach and, finally, the conformal mapping technique. The advantages and shortcomings of different methods will be discussed as well. The course does not assume any particular knowledge in hydrodynamics. It is therefore suitable for researchers and graduate students in applied mathematics and related fields.
