The Granule-In-Cell Method for Simulating Sand–Water Mixtures

The simulation of sand-water mixtures requires capturing the stochastic behavior of individual sand particles within a uniform, continuous fluid medium. However, most existing approaches, which only treat sand particles as markers within fluid solvers, fail to account for both the forces acting on individual sand particles and the collective feedback of the particle assemblies on the fluid. This prevents faithful reproduction of characteristic phenomena including transport, deposition, and clogging. Building upon kinetic ensemble averaging technique, we propose a physically consistent coupling strategy and introduce a novel Granule-In-Cell (GIC) method for modeling such sand-water interactions. We employ the Discrete Element Method (DEM) to capture fine-scale granule dynamics and the Particle-In-Cell (PIC) method for continuous spatial representation and density projection. To bridge these two frameworks, we treat granules as macroscopic transport flow rather than solid boundaries within the fluid domain. This bidirectional coupling allows our model to incorporate a range of interphase forces using different discretization schemes, resulting in more realistic simulations that strictly adhere to the mass conservation law. Experimental results demonstrate the effectiveness of our method in simulating complex sand-water interactions, uniquely capturing intricate physical phenomena and ensuring exact volume preservation compared to existing approaches.