# A Simulation Method for Layered Filling of Grain Piles Based on the Discrete Element Method
###### Abstract  
The Discrete Element Method (DEM) has been widely employed to investigate the behavior of particle systems at a macroscopic scale. However, effectively simulating the gradual filling of bulk cereal grains within silos using the DEM remains a formidable challenge due to time constraints. Thus, there is a critical need to develop a simplified model capable of substantially reducing the computational time required for simulating cereal grain accumulation. This study introduces a Layered Filling Method (LFM) designed to expedite the computational process for cereal grain piles within silos. By utilizing particle kinetic energy as a specific criterion, this model identifies particles as stable situations when their kinetic energy drops below a designated threshold. Throughout the filling process, lower particles that were judged to satisfy the condition of stability are isolated, forming sub-heaps that are exempt from persistent detection. The whole particle heap is subsequently segregated into multiple sub-piles and a main pile till the process's culmination, and these divisions are merged back together. In order to validate the model's feasibility and accuracy, a comparative analysis was performed on the characteristics of the porosity and airflow patterns of grain piles generated using the LFM and the progressive filling method (PFM), respectively. The research results indicate that there is a marginally higher porosity value in the grain pile simulated by the LFM in comparison to the PFM. However, the average relative error remains below 5.00%. Both the LFM and PFM exhibit a similar spiral upward trend in the simulated airflow paths. Notably, the LFM demonstrates a substantial reduction in the time required to construct grain piles. D 2023 13 11347 10.3390/201  
Another approach to reduce computation costs is to simplify the DEM, which involves modifying the geometric and physical properties of the simulated particles. Some researchers have employed the technique of modifying particle sizes to decrease the overall number of particles that are required for computation [13; 14; 15], thus enabling longer time steps. [PERSON] explored the effectiveness of the Scale-Up Particle (SUP) model in reducing computational requirements [16]. The number of particles to be considered is reduced by scaling them up proportionally when the occupied space is much larger than that occupied by the particles under investigation. Additionally, other researchers have simplified the model by altering particle properties rather than the sizes or shapes [17; 18; 19]. He achieved accelerated simulation speed by reducing the stiffness of particles in additive manufacturing simulations [20]. For some simulations, another way to reduce the computation cost is to simplify the generation process of the particles under study. [PERSON] analyzed the differences between the PFM and the global filling method. The PFM that simulates the actual particle storage process is closer to reality than the mass filling method [21]. While the aforementioned methods have been adopted to reduce computational costs, the simulation cost of a huge grain pile in a silo still exceeds the acceptable time range. Consequently, reliance on empirical formulas for porosity distribution in ventilation simulations has become prevalent [22; 23]. This method is simple and reliable to implement, but at the same time, it causes obvious deviations from the actual situation. If reducing the calculation cost of the DEM is available, it is possible to apply almost the real porosity distribution in the ventilation simulation of large granaries. To address the challenge of reducing computational burden in simulating grain particle accumulation within silos, this study introduces the Layered Filling Method (LFM). The overall thinking of this method is that the particles can be considered stable when the kinetic energy is below a certain threshold.