Verlet buffer for broad-phase interaction detection in Discrete Element Method

The Extended Discrete Element Method (XDEM) is a novel and innovative numerical simulation technique that extends the dynamics of granular materials or particles as described through the classical discrete element method (DEM) by additional properties such as the thermodynamic state, stress/strain for each particle. Such DEM simulations used by industries to set up their experimental processes are complex and heavy in computation time.
Those simulations perform at each time step a collision detection to generate a list of interacting particles that is one of the most expensive computation parts of a DEM simulation. The Verlet buffer method, which was first introduced in Molecular Dynamic (MD) (and is also used in DEM) allows to keep the interaction list for many time step by extending each particle neighborhood by a certain extension range, and thus broadening the interaction list. The method relies mainly on the stability of the DEM, which ensures that no particles move erratically or unpredictably from one time step to the next: this is called temporal coherency. In the classical and current approach, all the particles have their neighborhood extended by the same value which leads to suboptimal performances in
simulations where different flow regimes coexist. Additionally, and unlike in MD (which remains very different from DEM on several aspects), there is no comprehensive study analyzing the different parameters that affect the performance of the Verlet buffer method in DEM.
In this work, we apply a dynamic neighbor list update method that depends on the particle's individual displacement, and an extension range specific to each particle and based on their local flow regime for the generation of the neighbor list. The update of the interaction list is analyzed throughout the simulation based on the displacement of the particle allowing a flexible update according to the flow regime conditions. We evaluate the influence of the Verlet extension range on the performance of the execution time through different test cases and we empirically analyze and define the extension range value giving the minimum of the global simulation time.