## 1 Introduction
To significantly decrease the number of tracked particles and thus the associated computational cost, a coarse grain model of the DEM was developed by [PERSON] et al. [30; 31]. This coarse grain model treats a group of original particles with similar properties as a large-sized particle, generally termed as a coarse grained particle, a parcel or a particle-group. It allows for simulating of industrial scale systems with acceptable accuracy using practical amounts of computational resources and time. In previous studies, the coarse grain DEM-CFD model was adequately verified in gas-solid flows [30; 31; 32; 33; 34; 35; 36]. In these studies, the flow properties including minimum fluidization velocity, bubble velocity, bed height and bed pressure drop were well predicted by the coarse grain DEM-CFD model. According to increasing the coarse grain ratio, which is defined to be the ratio of particle-group size to original one, the simulation cost and the accuracy are decreasing simultaneously, so the coarse grain ratio should be properly chosen for the coarse grain DEM-CFD model. Even though the coarse grain DEM-CFD model is verified in many applications, it is imperfect. In this model, the original particles are treated as particle-groups based on the initial particle distribution, and during the whole simulation process the number and components of these particle-groups remain unchanged. However, because of collisions during the real physical process, an original particle may escape from the particle-group which contains it or adhere to the original particles belonging to another particle-group. This fact obviously can lead to frequent crushing and polymerization of particle-groups. But the current coarse grain DEM-CFD model ignores this important physical process. Consequently, its ability for describing the heterogeneity caused by the complex mesoscale structures of gas-solid systems may be not enough. The system is likely to be overly averaged due to the unchangeable statistical averaging done at the beginning of the simulation. The purpose of this paper is to rationalize the coarse grain DEM-CFD model by considering the dynamic particle-group crushing and polymerization to overcome the unrealistic coarse grain treatment of particles. In particular, the effective size of each particle-group is measured by a quantity called the equivalent particle-group diameter, whose definition references the equivalent cluster diameter used by the energy-minimization multi-scale (EMMS) model [37; 38]. Then a particle-group crushing criterion is presented based on the mismatch between the equivalent diameter and actual diameter of a particle-group. As to the polymerization of two colliding particle-groups, their velocity difference after collision is chosen as a criterion. Moreover, particle clusters can be induced by the complex gas-solid flow. Once a particle cluster is formed, the local fluidized behavior will be greatly changed. The flowing gas is more likely to bypass the particle cluster rather than go through it. Therefore, the drag force acting on the particle cluster will be less than the summation of those acting on the individual particles. That is the drag force drop observed in experiments [39]. Considering the flow heterogeneity induced by the particle cluster formation, the EMMS drag force model is used in this work to predict the drag force drop in case of particle clustering. Simulation results show that the proposed dynamic coarse grain DEM-CFD model is more accurate than the previous one.