Free surface waves in a wave tank

We consider the motion of an inviscid and incompressible fluid in an closed or semi-infinite basin with free surface waves. An intrinsic feature of the problem is the formation of waves by a periodic motion of one part of the boundary of the basin. Sharp corners of the rectangular domain and between the free surface and the side walls of the basin are critical regions of the solution. The correct formulation and solution of the problem in these regions is necessary for the simulation of the free surface waves in a bounded domain. We formulate compatibility relations for the dynamic contact lines as necessary conditions for the existence of a solution to the free boundary problem for a potential flow. We derive a formulation and numerical solution in a compact way so that natural compatibility conditions can be satisfied at the interface between the walls of the basin and the free surface.