Moiseev's procedure (1958) is used to derive a combined numerical and analytical method for sloshing in a general two-dimensional tank with vertical sides at the mean waterline. It is shown that the latter restriction follows from conservation of fluid mass. A low-order panel method based on Green's second identity is used as part of the solution. The method is verified by comparison with the analytical solution by Faltinsen (1974) for a rectangular tank shape. It is demonstrated that more than 100 elements may be needed to describe the free surface in the panel method.

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