Higher-order MPS models and higher-order Explicit Incompressible MPS (EI-MPS) method to simulate free-surface flows

In this study, higher-order spatial models including the gradient model and Laplacian model based on Taylor's series and using their coordinates as coefficients are evaluated by calculating some simple functions and a diffusion problem. The numerical convergence is achieved by the models as the smaller particle distance can calculate more accurate results. By using the models, when the particle distribution is significantly irregular, increasing the search radius can involve more neighboring particles which consequently improves the accuracy. Based on the proposed higher-order models, the higher-order Explicit Incompressible version of the Moving Particle Semi-implicit method (EI-MPS) is developed. The numerical scheme is validated by simulating various free surface flows including the rotation of a fluid square patch, the impact of two identical rectangular fluid patches, oscillating drop under a central force field, a hydrostatic problem, and dam-break flow. The parameters of the particle distance, search radius, and repeated time in the pressure calculation are all examined in the free surface flows. The proposed method can reproduce the free surface variations, kinetic energy, and total energy variation in the violent flows. It can also obtain the hydrostatic pressure achieving numerical convergence. Increasing the search radius can result in larger errors in simulating the hydrostatic pressure. The impacting pressure caused by the dam-break flow is reflected by the method in good agreement with the experimental measurements.