Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations are widely used to investigate gas-solid flow behavior in fluidized beds. These flows manifest dynamic meso-scale structures that span a wide range of spatial and temporal scales. These structures can be resolved by CFD-DEM simulations in small computational domains. However, the computational cost to resolve them in simulations of flows in large industrial units is prohibitive, where coarse-grained simulation approaches such as CFD-DPM (discrete parcel method) and MP-PIC (multi-phase particle-in-cell) are more viable [1,2,3]. In these coarse-grained simulations, only a small number of representative particles (a.k.a. “parcels”) are simulated and particle-particle interaction is treated via tracking collisions between particles  or a physically reasonable particle phase stress model [2,3]. In previous studies of our group [5,6], we proposed the coarse-grained fluid-particle drag relation for coarse CFD-DEM/DPM and MP-PIC simulations of industrial scale gas-particle flows. The goal of the present study is to provide the particle stress model for coarse MP-PIC simulations. We first performed highly resolved CFD-DEM simulations of gas-fluidization of mono-disperse particles in periodic domains at various solid volume fractions. By following the particle coarsening methodology given by , the results are analyzed to formulate an effective particle phase stress model. This model is then assessed in a posteriori manner through crossing jets and Taylor-Green vortex flow test cases.
 M. Sakai, H. Takahashi, C.C. Pain, J. Latham, and J. Xiang, “Study on a large-scale discrete element model for fine particles in a fluidized bed” Adv. Powder Technol., 23 (2012).
 D. M. Snider, “An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows”, J. Comp. Phys., 170, 523 (2001).
 P. J. O’Rourke, and D.M. Snider, “An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets”, Chem. Eng. Sci., 65, 6014 (2010).
 N.A. Patankar, D.D. Joseph, “Lagrangian numerical simulation of particulate flows”, Int. J. of Multiphase Flow, 27, (2001).
 S. Radl, S. Sundaresan. "A drag model for filtered Euler–Lagrange simulations of clustered gas–particle suspensions." Chem. Eng. Sci. , 117, (2014).
 A. Ozel, S. Radl, S. Sundaresan, ‘Effective Drag Model for Euler-Lagrange Simulations of Gas-Fluidized Beds’, AIChE Annual Meeting, Atlanta, Georgia, (2014).
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