Material point method and smoothed particle hydrodynamics simulations of fluid flow problems: a comparative study

The material point method (MPM) and the smoothed particle hydrodynamics (SPH) are two commonly used particle-based methods for solving large-deformation problems. Especially, the SPH has been widely applied to fluid dynamics problems, while the MPM performance in fluid dynamics simulations has rarely been investigated. In this study, the capabilities of the MPM and the SPH in simulating fluid dynamics problems have been quantitatively examined and compared through three example problems, i.e., Poiseuille and Couette flows and water dam break flows. Both numerical methods could yield the results in good agreements with the theoretical and experimental results. Without requiring neighbour search and additional boundary particles, the MPM exhibits significantly higher computational efficiency as compared with the SPH. The comparisons also demonstrate that the MPM has higher accuracy and faster convergence than the SPH. It is shown that the MPM could be a promising alternative to the SPH for the fluid dynamics simulations. Future work for the improvement of the MPM in fluid dynamics modelling is discussed.