A coupled SPH-DEM approach for modeling of free-surface debris flows

A Lagrangian mesh-less model is proposed to simulate fluid–solid flows with multiple-sized solids, i.e., millimeter-sized particle and larger-sized debris. Considering the difference in the size of solid phases, a hybrid resolved and unresolved model is established based on the coupling method of smoothed particle hydrodynamics (SPH) and discrete element method (DEM). SPH is used to model fluid, and the locally averaged Navier–Stokes equations are adopted as governing equations. DEM is used to model the particle–particle interactions, and the unresolved description of hydrodynamic forces including drag and buoyancy is established. The large-sized debris is modeled as the rigid body, which is discretized by particle elements having both SPH and DEM characteristics, where SPH particle elements are involved in the closure of the SPH fluids, and DEM particle elements interact with the solid particles following the contact law. The numerical model is validated and verified by several examples, including single-particle sedimentation, collapse of cylinder columns, and debris dam break. Results show that the present model reproduces general features of the complex fluid–solid flow with free surfaces. The advantage of the hybrid model is that it can deal with the fluid–solid flow problem with both small particles and large objects at a suitable resolution, and it is especially good at dealing with the free surface flow problem. A discretization for the modeling of debris flows is proposed based on the coupled SPH-DEM method. The novelty of the work is a coupled resolved–unresolved scheme for the free surface flow with multi-sized solids. The present scheme allows using a uniform resolution by bridging the size difference between small-scale solid particles and large-scale debris. The unresolved model of fluid-particle flow is efficient because the fluid resolution can be configured comparably to the particle size. The unified nature of the model allows the combination of resolved and unresolved simulations in the same computational domain.