Dense particulate flow model on unstructured mesh

A numerical method based on two-dimensional (2D) unstructured meshes is developed to solve the discrete particle model (DPM). Inter-particle interactions are taken into account for dense particulate flows, which are described by binary collisions in a hard-sphere model. The particle volume fraction is calculated accurately and physical scalars from the Eulerian grid to the Lagrangian particle positions are mapped through gradient interpolations. The governing equations for the continuous phase are discretized using a finite volume method on an unstructured grid and solved by the algebraic multi-grid (AMG) method. The SIMPLE algorithm employed to solve single-phase flows on unstructured meshes is extended to the pressure–velocity equations. Momentum coupling between the two phases is strongly implicit resulting in a very robust convergence of the AMG solver. Data structuring and mapping techniques for further enhancement of the flexibility and computational efficiency of the numerical model are introduced. Several test cases confirm that the numerical method can be applied to gas–solid and gas–liquid flows in irregular domains without regard to element types of the mesh. The numerical model presented in this paper partly overcomes the difficulties in simulating dense particulate flows using the DPM in 2D irregular domains.