A mixture model for simulating particle-laden flows with the Particle Finite Element Method

Particle-laden flows are fundamental in numerous engineering fields, including environmental hydraulics, sediment transport, and process engineering, where understanding the interaction between fluid and particulate phases is critical for design and prediction. This work presents a novel mixture model for sediment transport within the Particle Finite Element Method (PFEM) framework. The model couples the Navier–Stokes equations for fluid flow with a transport-diffusion equation for sediment concentration, treating sediment as a scalar field rather than discrete particles. This approach enables efficient simulation of fluid–sediment interactions without the computational cost of tracking individual sediment particles and their contacts. PFEM’s Lagrangian nature allows the mesh to follow the flow motion, with remeshing strategies implemented to maintain mesh quality during large deformations. The model incorporates both Neumann and Robin boundary conditions for sediment concentration, enabling a realistic representation of sediment deposition and exchange at fluid–bed interfaces. Validation is conducted through two- and three-dimensional test cases, including channel flows, gravity current intrusion with multiple fluids, and sediment deposition in tanks with orifices. Comparisons with experimental data and particle-based simulations demonstrate that the model captures key sediment transport phenomena accurately under low-concentration conditions. The proposed mixture model offers a robust and computationally efficient tool for simulating sediment-laden flows in engineering applications.