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

The Extended Discrete Element Method (XDEM) is an innovative numerical simulation technique that extends the dynamics of granular materials known as 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 complexes and heavy in computation time.
At each time step, those simulations generate a list of interacting particles and this phase is one of the most computationally expensive parts of a DEM simulation. The Verlet buffer method, initially introduced in Molecular Dynamic (MD) (and also used in DEM), allows keeping the interaction list for many time steps by extending each particle neighbourhood by a certain extension range, and thus broadening the interaction list. The method relies on the temporal coherency of DEM, which guarantees that no particles move erratically from one time step to the next. In the classical approach, all the particles have their neighbourhood extended by the same value which leads to suboptimal performances in simulations where different flow regimes coexist. Additionally, and unlike in MD, there is no comprehensive study analysing the different parameters that affect the performance of the Verlet buffer method in DEM.
In this work, we propose a new method for the dynamic update of the neighbour list that depends on the particles individual displacement and define a particle-specific extension range based on the local flow regime. The interaction list is analysed throughout the simulation based on the particle's displacement allowing a flexible update according to the flow regime conditions. We evaluate the influence of the Verlet extension range on the execution time through different test cases and analyse empirically the extension range value giving the best performance.