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Unsteady two-dimensional flows which have a free boundary are examined numerically. The fluid is considered to be irrotational and incompressible and the boundary is assumed to have a continuous tangent. The use of numerical techniques enables one to treat the nonlinear problem and to include those cases in which the streamlines intersect the boundary. The technique is quite accurate and calculations are required only on the boundary of the fluid.

A numerical model of the unsteady free boundary of an ideal fluid