A comparative study of reinitialization approaches of the level set method for simulating free-surface flows

Abstract

Unstructured grids were used to compare the performance of a direct reinitialization scheme with those of two reinitialization approaches based on the solution of a hyperbolic Partial differential equation (PDE). The problems of moving interface were solved in the context of a finite element method. A least-square weighted residual method was used to discretize the advection equation of the level set method. The benchmark problems of rotating Zalesak’s disk, time-reversed single vortex, and two-dimensional sloshing were examined. Numerical results showed that the direct reinitialization scheme performed better than the PDE-based reinitialization approaches in terms of mass conservation, dissipation and dispersion error, and computational time. In the case of sloshing, numerical results were found to be in good agreement with existing experimental data. The direct reinitialization approach consumed considerably less CPU time than the PDE-based simulations for 20 time periods of sloshing. This approach was stable, accurate, and efficient for all the problems considered in this study.