SUMMARYThis paper presents a numerical method for free surface ows that couples the incompressible NavierStokes equations with the level set method in the ÿnite element framework. The implicit characteristicGalerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are veriÿed with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular uid element. The results are compared with those calculated from the level set ÿnite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853 -884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier-Stokes solver is conÿrmed by simulation of decay vortex. The coupled system of the Navier-Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data.

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