An FEM-Level-set Numerical Model for Potential Flow with Free Surface

A Level-set and Finite Element Method (FEM) based two-dimensional numerical model is proposed for the free surface flows in the frame of potential theory. The FEM is used to solve the governing equation of potential flow while the Level-set method is used to capture the free surface. A new numerical technique is proposed to treat the partial elements that are cut by the free surface. Fully nonlinear boundary condition is used on the free surface. During the simulation, Eulerian meshes are adopted and only the fluid phase is calculated. A linear sloshing problem is firstly used as a benchmark to check the accuracy of the FEM solver. The numerical results are compared with the theoretical solution, and good agreements are obtained. Then the dam breaking flow with violent free surface is used to validate the proposed FEM-Level-set model. The comparisons show that present model has good numerical stability, and is able to produce reasonable prediction on the free surface evolution. Finally a fully nonlinear sloshing problem is simulated. The numerical results of the present model agree well with those obtained by the model based on boundary element method.