## 1 Introduction
In addition to the mechanism of neutronics for evaluating the criticality safety, the thermal hydraulics in the fluid phase, the heat transfer between the particles, and the momentum/energy transfer between particle-fluid phases also should also be taken into account for conducting the cooling characteristics assessment of a decay heat-generating porous bed, as shown Figure 1. Moreover, the importance of the multi-physics interplay is further increased when considering dynamic particle redistribution into the debris bed's safety assessment. For example, dynamic particle redistribution can address the extra effect on the flow velocity distribution and following heat convection capability, which can further affect the temperature distribution of the solid  
Figure 1: The schematic of the mechanisms regarding the debris bed safety assessment under the scenario of heterogeneous particle redistribution. particles and coolant fluid. On the other hand, the altered flow velocity distribution can also address the effects of the subsequent particle movement by the solid-fluid interfacial force, subsequently contributing to the heterogeneous configuration transformation, whose effect will be further reflected in the neutronics calculation. The transience with complex multiphysics interplay phenomena makes it hard to measure all the required timely data for criticality/cooling analysis simultaneously via experimental approaches; therefore, numerical analysis could be a suitable alternative to capture the main physical features along the transient time domain and yield the assessments in a broad spectrum, which was selected as the main direction of this study. However, the typical numerical method used to conduct thermal-hydraulic analysis in the fluid phase, Computational Fluid Dynamics (CFD), which assigns the area of the particulate bed as the homogeneous porous media by applying the empirical pressure drop model [30], has the inherent limitation that the particles are assumed to have stationary status, and Monte-Carlo-based Neutronics (MCN, to conduct neutronic analysis) are under the same limitation. This can also cause the effect of the multi-physics interplay accompanied by particle redistribution being unable to be integrated into the bed safety assessment. Hence, in order to realize the purpose of this research when considering the interaction of multi-physics, a newly coupled methodology is proposed here by incorporating the Discrete Element Method (DEM) with CFD and MCN methods, which is free from the constraint of the static particle conditions and even accessible for the scenario of the debris bed's heterogenous configuration transformation under particle redistribution when considering the multi-physics interaction between the criticality/cooling analysis. The characteristics of the coupled elements are explained below:  
* DEM, a Lagrange-based analytical method developed by [PERSON] and [PERSON] for considering multi-body collision and movement [31], is suitable for simulating particle redistribution. In addition, since DEM can introduce individually heterogeneous solid DEM particles into the computational domain, it can reproduce various heterogeneous configurations, and should be allowed to consider the heat conduction transfer between solid particles;
* CFD is the Eulerian-based method for conducting thermal-hydraulic analysis in the fluid phase. Additionally, the momentum exchange (e.g., drag force, buoyancy) and energy exchange (e.g., heat convection transfer) between fluid and solid particle can also be estimated using sub-models based on the calculated information from both CFD the DEM sides, which also contributes to the further effect on the subsequent heterogeneous configuration's transformation, predicted in the DEM side;
* Because of its flexible geometry description capability, MCN can construct highly sophisticated and heterogeneous geometries in detail, and it is possible to reflect information from both the CFD and DEM sides to perform neutronic evaluations for the debris bed's criticality analysis.