  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.
