This paper presents an advanced level set method for the analysis of time-dependent free surface movement. Three-dimensional numerical simulations of mercury sloshing phenomena based on the GSMAC-FEM are carried out with the amplitude of 1.00×10{sup}（-3） m and the frequencies of 1.3, l.8Hz. Moreover, the GSMAC-CIP method is applied to advection equations for the accurate calculation. The results are compared with the ones of the ALE method, and they show good agreement in terms of time histories of surface waves. These results are also in accord with the linear theory qualitatively.
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