A background grid enriched incompressible SPH method for free surface flow problems modeling

We propose a background grid-enhanced incompressible smoothed particle hydrodynamics method (BG-ISPH) for simulating free surface flow problems. The pressure Poisson equation (PPE) is computed by employing a background grid-based method, while the momentum equations are solved using the SPH method. The presented BG-ISPH method benefits from the advantages of both types of numerical approaches: the grid-based method enables efficient and accurate calculation of the pressure; meanwhile, the advantages of the SPH method in handling free surface problems with large deformations are preserved. Consequently, this approach improves the stability and numerical accuracy compared to the traditional ISPH method. We applied this model to simulate a series of benchmark problems involving different types of free surfaces and compared the numerical results with experimental observations and other simulation results in the literature. Additionally, we investigate the influence of background grid size on the model’s accuracy and propose an optimal grid-to-particle size ratio range of 1.0–1.75. The results demonstrate the stability and accuracy of the BG-ISPH model in simulating free-surface flow problems.