Coupled CFD-FEM approach for dense particle-fluid flows

• A fully Eulerian, two-way-coupled CFD-FEM framework is proposed • Granular stress model, incorporating μ ( I ), E ( ε s ), and P v , is introduced • E ( ε s ) allows particle state across dilute-dense regimes • Validated by packed bed, spouted bed, collapse, and cohesive silo jamming cases • CFD-FEM can capture stress redistribution and arch formation Particle-fluid flows are ubiquitous in natural and industrial processes, yet their modeling remains challenging due to the coexistence of flowing and quasi-static granular regions and the computational demands of large-scale systems. The Discrete Particle Method (DPM) offers particle-scale resolution but is computationally prohibitive for large domains. Conversely, the conventional Two-Fluid Model (TFM), while efficient, fails to capture essential features of dense regimes, including stress anisotropy, internal stress transmission, and quasi-static deformation. This study develops a fully Eulerian, two-way-coupled CFD-FEM framework that couples the Navier-Stokes equations for the fluid phase with a visco-elastoplastic model for the granular phase on a shared mesh. The solid phase is governed by an advanced constitutive law incorporating rate-dependent rheology μ ( I ), nonlinear elasticity E ( ε s ), and volumetric dissipation P v . In particular, an elasticity-porosity relation for E ( ε s ) extends the elastoplastic FEM to dilute particle states, enabling a unified dilute-to-dense treatment. Interphase coupling is achieved through momentum exchange and local solid volume fraction, enabling a robust, physically consistent, and scalable treatment of dense multiphase dynamics. The framework is validated against four benchmark cases—packed beds, spouted beds, column collapse, and cohesive-particle silo discharge (jamming)—demonstrating accurate prediction of pressure drop, faithful reproduction of central bubbles and recirculation zones, and the ability to capture stress redistribution, arch formation, and the transition between flowing and quasi-static states. Overall, the method provides a unified and scalable platform for simulating dense particle-fluid flows across a wide range of flow regimes.