Incompressible material point method for free surface flow

In computational fluid dynamics (CFD) and hydrodynamics, free surface flow is always a hot issue. In this paper, an incompressible material point method (iMPM) is proposed based on operator splitting in which the solution of the momentum equation is split into two steps. The pressure term is ignored first, and the predicted velocities can be obtained by solving the momentum equations without the pressure term. Then, the pressure term is used to correct the predicted velocities, and the corrected velocities must be divergence free. To better track the free surface, the level set function that calculates the signed distance to free surface is adopted. Hourglass damping is introduced to eliminate the spurious velocity mode inherent in the traditional MPM semi-staggered grid. Finally, the proposed method is verified by various test examples, which show that the proposed incompressible material point method is a powerful tool for solving free surface flow problems.