Fractional-step finite element method for calculation of 3-D free surface problem using level set method*

A two-step Taylor-Galerkin fractional-step finite element method, which is of second order accuracy in space and time, was proposed for the three-dimensional free surface problem. With this method, the intermediate velocity was explicitly obtained by neglecting pressure gradient term, and then the velocity was corrected by adding the effects of pressure once the pressure field had been obtained from the pressure Poisson equation. The level set approach was applied to track implicitly the free surface. In order to track the free surface, the transport equation of the level set function was solved at each time step and the level set function is reinitialized through iteration to maintain it as a distance function. The governing equations of the system were discretized by the two- step Taylor-Galerkin method, which is of high-order accuracy and easy to be used. The validity and reliability of this method in this article were proved by two numerical examples.