## 3 Discharge Simulation
### CEL Modeling  
The structure of the silo to be analyzed is shown in Figure 9a. The vertical wall section consisted of a cylindrical bunker with diameter d\({}_{c}\), and the hopper section was a conical hopper with hopper angle \(\beta\) and diameter d\({}_{0}\) orifice consisting of a total height H. The values for these geometric variables are listed in Table 3. The shape of the target silo was axially symmetric, and only 1/4 of the silo was modeled for efficiency in the numerical analysis. Because only 1/4 was modeled, plane symmetry  
Figure 8: An overview of the Coupled Eulerian–Lagrangian (CEL) method: (a): volume fraction tool; (b): CEL analysis; (c): remap procedure.  
conditions were applied to each side as shown in Figure 9b. In fact, it is noted that the load flow caused by silo material discharge may be asymmetric because of some transient influence, asymmetric arrangement, or operation. In this case, the above symmetric processing was invalid. However, in the case of a general cylindrical silos and conical hoppers such as those considered in this study, the computational time is effectively reduced by modeling only 1/4 of the target silos because a symmetric model is applicable.  
The silo discharge process simulation was performed using the CEL analysis method described in Section 3.2 using the commercial package Abaqus 2018. The silo wall and silo hotspot detector were modeled as rigid shells (element type R3D4), assuming that both the thickness and sag were negligible under the lateral pressure of the inner material. Translation and rotation were completely limited throughout the simulation. The material inside the silo was modeled using a 3D Eulerian element (EC3D8R) integrated with the basic hourglass control. The number of mesh was 8798.  
The procedures and boundary conditions used in the analytical modeling in this study are shown in Figure 8. To facilitate the identification of results such as stresses and velocities occurring near the silo wall, the computational mesh was constructed in the same shape as the silo and slightly increased in width to surround the silo wall. Figure 9b shows the mesh used in the simulation. For silo discharge analysis (or case) with different specifications, the FEM mesh should be changed accordingly. In the basic environment of the CEL method, the Eulerian element is free of materials. In other words, the element is occupied by \"voids\" (there are no physical properties in the void, but they are treated as materials in the Eulerian FEM system). Therefore, before starting the simulation, materials must be assigned to these silo elements as initial conditions, which is similar to the actual silo material filling process.  
As applied boundary conditions (Figure 9b), two Eulerian boundary conditions were created at the top and bottom of the structure so that the material could flow freely in and out of the computational space. As the analysis proceeded, the material flowed out because the discharge slowly replaced the voids from the top. The substances exiting the outlet were not considered in subsequent calculation steps because they were outside the calculation area.  
In summary, the silo discharge process simulating consists of four main steps: (i) creating silo walls, a silo hotspot detector, and Eulerian meshes using desired parameters; (ii) feeding material to  
Figure 9: Specifications for target structures (**a**), the discretization mesh used in the FEM (**b**).  
the expected levels of the mesh; (iii) applying boundary conditions and gravity as described; finally, (iv) running the simulation.