Development of a non-local partial Peridynamic explicit mesh-free incompressible method and its validation for simulating dry dense granular flows

In this study, a non-local partial Peridynamic mesh-free incompressible method is proposed for simulating dry dense granular flows such as granular column collapse. In the method, a predictor-and-corrector time splitting scheme is used, and Peridynamic theory is incorporated only in the predictor to solve an integrated momentum equation, in which part of the pressure gradient force, viscous force and external force are included. An incompressible explicit solver is employed to obtain the pressure field, and the corrector allows for the remaining part of the pressure gradient force to be calculated and updates the flow field. The proposed method is then validated by simulating granular flows in several configurations, including a steady granular flow down an inclined slope, granular column collapses at both one side and two sides, and collision of two adjacent granular columns. The simulated velocity profiles are in good agreement with the analytical solution in the steady granular down an inclined slope in which sensitivity of the particle distance, a coefficient by incorporating Peridynamics, and Peridynamic horizon are examined. The simulation of the granular column collapses shows that the method can reproduce the final deposit, free surface, and velocity in the flows. The method can capture interface variations between two granular columns during their collision in good agreement with experimental observations.

Automated summary

In this study, a non-local partial Peridynamic mesh-free incompressible method is proposed for simulating dry dense granular flows. The method incorporates Peridynamic theory in a predictor-and-corrector time splitting scheme to solve an integrated momentum equation. The proposed method is validated through simulations of various granular flow configurations, showing good agreement with analytical solutions and experimental observations.