Fluid–rigid-body interaction simulations and validations using a coupled stabilized ISPH–DEM incorporated with the energy-tracking impulse method for multiple-body contacts

In this paper, a new particle-based fluid–rigid-body interaction simulator for violent free-surface flow problems is developed. The incompressible Smoothed Particle Hydrodynamics (ISPH) method has been proven to produce a smooth and accurate pressure distribution of free-surface fluid flow with breaking and fragmentation. Computed hydrodynamic forces can be applied onto rigid bodies, which may simultaneously experience contact or impact with the surrounding wall boundaries or another rigid body. Modeled by using the discrete element method (DEM), the contact force between rigid bodies is traditionally calculated employing the penalty approach, where a spring-based repulsive force is approximated at the vicinity of contact points depending on the deepest penetration depth. However, for high-speed collision problems involving a system of many rigid bodies, the values of approximated repulsive forces may be highly overestimated, and thus, a much smaller time step and an excessive damping parameter are often required to stabilize the approximated forces. This problem is highly inefficient for the computational resources of the fluid–rigid body interaction simulation since the computational cost at each time step is mostly dominated by the incompressible fluid simulation. The capability to increase the time increment following the critical time step of the fluid solver is, therefore, strongly demanded to increase the simulation efficiency. The current paper incorporates the usage of the energy-tracking impulse (ETI) method as an alternative approach to handle contact accurately. To achieve better energy conservation and enhance stability, Stronge's hypothesis is considered instead of the generally assumed Newton's contact law. The current work also covers three experimental validation tests, which were conducted to assure the quality and robustness of the coupled ISPH–DEM implementation.