Modified incompressible SPH method for simulating free surface problems

An incompressible smoothed particle hydrodynamics (I-SPH) formulation is presented to simulate free surface incompressible fluid problems. The governing equations are mass and momentum conservation that are solved in a Lagrangian form using a two-step fractional method. In the first step, velocity field is computed without enforcing incompressibility. In the second step, a Poisson equation of pressure is used to satisfy incompressibility condition. The source term in the Poisson equation for the pressure is approximated, based on the SPH continuity equation, by an interpolation summation involving the relative velocities between a reference particle and its neighboring particles. A new form of source term for the Poisson equation is proposed and also a modified Poisson equation of pressure is used to satisfy incompressibility condition of free surface particles. By employing these corrections, the stability and accuracy of SPH method are improved. In order to show the ability of SPH method to simulate fluid mechanical problems, this method is used to simulate four test problems such as 2-D dam-break and wave propagation.