Granular media deformation and fluid flow as overlapping, concurrent, coupled multilayered depth-averaged framework

Abstract

A novel coupled depth-averaged formulation for the combination of multilayered fluid and monolayer granular flows as a set of interpenetrating continua has been developed in this study. Granular and fluid phases are coupled through an interaction force pair comprised of fluid stresses, and drag forces. Fluid phase is discretized in the vertical direction through a set N of virtual layer interfaces to obtain a variation of flow properties along depth. A novel algorithm for mass and momentum exchange between fluid layers for flow through and over porous media has been proposed. Eigenstructure analysis of the coupled system shows that the system may be discretized in N+1 separate yet coupled Riemann problems. An improved version of well-known HLL method is developed for solution of the model (Finite Volume Method) in a regular grid. The resistive source–sink terms are embedded implicitly within the interfacial flux. Based on the choices of state variables and layer-interface porosity, four variants of the coupled system are developed. A set of benchmark experimental test-cases and a representative test involving both rigid and deformable granular media has been simulated using the four variants to establish the robustness of the model and the coupling procedure.