Simulation of submerged granular flows by development of a two-phase incompressible explicit mesh-free method

Abstract

The interaction between fluid and sediment particles is widely involved in hydraulic engineering problems. In the current study, an explicit incompressible mesh-free method in the framework of the Moving Particle Semi-implicit (MPS) method is proposed to simulate the interaction between the two phases in submerged conditions. The proposed method solves two sets of the continuity and momentum equations, respectively, for the fluid phase and the sediment phase according to the mixture theory. In the method, the pressure and velocity fields are explicitly calculated for the sediment phase with the solid concentration obtained from the mixture theory, in which a rheology model is used to account for the viscosity and shear stress. The governing equations for the fluid are solved using the predictor–corrector time-splitting scheme and the resulting Poisson equation for pressure is calculated using an explicit scheme. In each loop, the discretized points move according to the velocity of the fluid in the mesh-free Lagrangian approach. The proposed method is used to simulate the submerged granular flows including submerged granular column collapse, submerged granular sliding on slopes, and erodible dam-break flow. In the simulations, the parameters of particle distance and collision distance in the numerical method are investigated. It is found that the flow characteristics in the granular flows are reflected by the proposed method and the simulated free surface and water–sediment interface profiles are in good agreement with experimental observations.