A direct reinitialization approach of level-set/splitting finite element method for simulating incompressible two-phase flows

Computation of a moving interface by the level-set (LS) method typically requires reinitialization of LS function. An inaccurate execution of reinitialization results in incorrect free surface capturing and thus errors such as mass gain/loss so that an accurate and robust reinitialization process in the LS method is essential for the simulation of free surface flows. In the present study, we pursue further development of the reinitialization process, which directly corrects the LS function after advection is carried out by using the normal vector to the interface instead of solving the reinitialization equation of hyperbolic type. The Taylor-Galerkin method is adopted to discretize the advection equation of the LS function and the P1P1 splitting finite element method is applied to solve the Navier-Stokes equation. The proposed algorithm is validated with the well-known benchmark problems, i.e. stretching of a circular fluid element, time-reversed single-vortex, solitary wave propagation, broken dam flow and filling of a container. The simulation results of these flows are in good agreement with previously existing experimental and numerical results.