Modified incompressible SPH method for simulating free surface problems using highly irregular multi-resolution particle configurations

In this study, the conventional incompressible smoothed particle hydrodynamics (I-SPH) formulations are modified to be applicable for highly irregular multi-resolution particle distributions for simulation of transient free surface flows. The modifications are based on distinguishing between particle density calculated by interpolation functions in SPH method and fluid density as a physical quantity. I-SPH is a fully Lagrangian method having great potential in dealing with large deformations of the free surface. Flow domain is discretized into a set of moving particles, and each particle carries mass, velocity and pressure during simulation time. Variations in these field parameters can be determined by temporal discretization of Navier-Stokes equation followed by a spatial discretization using I-SPH method. In addition to this, three pressure gradient models are employed for simulation of free surface flows to examine efficiency of the models coupled with the modifications. Furthermore, a simple and efficient method to find free surface particles which is compatible with highly irregular multi-resolution particle distributions is proposed. The modified approach is tested against different free surface problems using highly irregular particle configurations. The classic pressure gradient model employed in SPH method coupled with constant smoothing distance gives accurate results with lower computational times over highly irregular particle distributions. The method can be applied for adaptive refinement strategy to reduce computational times of transient free surface problems.