A new method is proposed in order to compute dynamic behaviours of a liquid free surface. The method is based on a discrete singularity method, and enables us to simulate sloshing problems very easily and efficiently. The authors consider the free surface in a two-dimensional rectangular container that is vibrated vertically. It was found that there is the optimum clearance of singularity from a boundary, which makes surface error minimum. Furthermore, the authors conducted some experiments, and have observed three sloshing modes, and their stability regions. Then, we confirm that for the method is effective for 2D-sloshing problems.

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