Irregular points in 2-D free surface flows with surface tension for the wavemaker boundary value problem

Oscillatory, two dimensional free-surface, irrotational flows of an incompressible fluid are treated numerically. Rather than basing the treatment on perturbation expansions, the unknown fluid domain bounded by a free surface is mapped onto a rectangular domain. This has the effect of exchanging a boundary value problem for a linear, constant coefficient Laplace equation having nonlinear boundary conditions into a nonlinear elliptic equation specified on the known rectangular domain. In the known transformed domain, compatibility conditions at the corners are derived, the boundary value problem is solved and the results are transformed back to the original domain.