A numerical solution to a free surface wave problem (Q1922776)

The authors consider free surface waves of water in a rectangular basin which are caused by a movig wall. First, they derive a formulation of the problem as a system of nonlocal partial differential equations of first order for the free surface and the velocity potential. This last system splits the problem into a linear and a nonlinear part. The linear part is formulated in a time-dependent domain, whereas the nonlinear part describes the velocity potential and the free surface in a fixed domain. Then, using highly efficient implicit methods for the solution of a corresponding semi-discretized system of ordinary differential equations, the authors can solve the problem ensuring natural compatibility conditions at the interface between the fluid and the boundaries.