Simulating Free Surface Flows Using a New Incompressible SPH Model Improved by MPS Method

Performance of a new incompressible smoothed particle hydrodynamics (I-SPH) model for simulating free surface flows using Lagrangian description of motion is numerically evaluated. In the SPH method, kernel or weight functions are used for approximation of a function and its spatial derivatives based on the theory of integral interpolants exhibiting poor accuracy. In this study, the pressure field is obtained by solving a pressure Poisson equation that is derived from a two-step prediction-correction approach applied for temporal discretization of the governing equations of fluid flows and enforcement of incompressibility. A newly developed gradient model in the context of the mesh-less moving particle semi-implicit (MPS) method is applied to improve the standard gradient and Laplacian models of I-SPH method in the proposed approach. The higher accuracy of the modified SPH scheme, which is a kernel gradient-free model, in comparison with the standard I-SPH method is validated trough solving the classic benchmark problems including the dam break flow, solitary wave propagation, standing wave motion, liquid sloshing and water drop stretching.