Abstract: For incompressible flows, there are two kinds of moving boundary problems, i.e. the steady case, such as the over-gate flow with constant elevation, spillway, wiers and jet flows; the unsteady case, sueh as the liquid sloshing in a container. The principal difficulty of these problems lies in the undetermined free surfaces, where an iterative scheme has to be used together with the correction of the network in computation. In particular, the computational effort will be considerable because of the strong no...