## 1 Introduction  
In plants using coal or biomass fuels, there is always a risk of fire due to the spontaneous combustion of silo [1]. As a countermeasure against this, IR cameras and gas detectors are used to prepare for fire in order to detect the natural ignition of the silo in advance [1]. However, since the start of spontaneous ignition starts with the increase in the temperature of the center of the silo, it is difficult to detect the starting point of spontaneous ignition by measuring the temperature of the silo surface through an IR camera or measuring gas leakage through a gas detector. The silo hotspot detector, which can measure the temperature of each level, developed for this purpose, is installed inside the silo and monitors the internal temperature in real time to prevent fires caused by spontaneous ignition. However, the silo internal material is frequently charged and discharged, and the pressure and tensile force generated therefrom also frequently changed. If the silo hotspot detector is destroyed by this, it will cause a big accident, so it is necessary to check the possibility of the silo hotspot detector destruction due to the discharge of material inside the silo. The pressure and load on an internal structure caused by material discharge is governed by the flow of material. The flow of material inside silo is a phenomenon that occurs in many industrial applications; this phenomenon has unique flow and stress characteristics, and it must be considered when designing a device that meets operational and safety requirements. The study of the flow of material has been an active topic of study over the past century [2; 3; 4; 5]. [PERSON] [6] and [PERSON] [7; 8] described the general flow of material inside a silo. However, the method of accurately evaluating the stress field and material discharge rate occurring inside the silo remains a popular research topic. This is because the theory described by [PERSON] and [PERSON] is limited to silos that have a shape where the silo outlet and the center line of the hopper coincide. However, silos that do not actually meet this condition are also used in many industrial fields [9]. Even in silos with specific conditions, accurate evaluation may not be possible based on the scenario. [PERSON] et al. [10] suggested that, as assumed by the pressure theory [6; 11; 12], the theory is applicable only to steep hoppers, as the wall friction effect of these hoppers develops completely during outflow. For shallow hoppers in which the wall friction develops only partially, significant modifications to the theory are required. Discrete and continuum numerical methods are commonly used to model and simulate the flow of materials. The discrete element method (DEM) achieves particle-scale simulation and simulates the motion of each individual particle under certain conditions. Furthermore, it can provide micromechanical information such as trajectories and transients acting on individual particles. Therefore, the DEM has been increasingly used to study phenomena and behaviors occurring in hoppers such as mass flow rate [13], particle flow pattern [14], and internal bulk stress [15; 16]. However, DEM simulation is computationally demanding and can handle only small systems. Methods such as multidomain continuum and other discrete methods [17; 18; 19] have been proposed to solve these problems; however, there remains difficulties in using DEM simulation with large systems. In the continuum type method, the dynamics of the material are governed by the momentum and energy conservation equations, and the flow is modeled on a macroscopic or global scale, with a construction model describing the unique properties of the material. The finite element method (FEM)--a continuum approach--has been used in hopper studies. Thus, hopper internal stress and wall pressure have been predicted satisfactorily. However, to simulate the flow conditions of a material, specific techniques or treatments such as remeshing and rezoning plans [20] and adaptive meshing techniques [21] are required.