Abstract
The unsteady motion of a sharp interface in the irrotational flow of an incompressible, inviscid fluid is about the simplest mathematical model of the motion of a transitional layer between two continuous fluid media. Even such a model provides challenging problems to the mathematician and computer among others. The difficulties arise from the non-linear nature of the equations; the interior flow affects the free surface motion, which affects the interior flow. This type of non-linearity makes the analysis difficult but provides the richness of phenomena observed in free surface flow. In general, numerical techniques must be used to compute free surface motion. There are several different methods that might be adopted. Boundary integral techniques are among the most useful because they are naturally adaptive in the sense that only information at the surface is used in the calculations. Their apparent disadvantages are twofold. They are presently limited to those cases where the interior flow is creeping or incompressible, irrotational, and inviscid; and they require solutions to integral equations that can be expensive to compute.
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