An Unstructured Level Set Method for Free Surface Flows

We present a numerical method that couples the incompressible Navier-Stokes equations with the level set method on an unstructured mesh for study of free surface flows. The Taylor-Galerkin finite element method together with the fractional four-step algorithm is employed to discretize the governing equations. The subroutines for solving the level set equations of evolution and reinitialization are verified with several benchmark cases. We also compare this method with the structured level set finite volume method of Yue et al. (Int. J. Numer. Meth. Fluids, 42: 853-884, 2003), that implemented the third-order TVD Runge-Kutta scheme for time marching and the third-order essentially non-oscillatory scheme for spatial discretization of the level set equations. The results show that the Taylor-Galerkin approach yields excellent solutions. The coupled system is then applied to the two-dimensional dam breaking problem for code validation. The results are in good agreement with experimental data.