Volume-Preserving LBM-MPM Coupling for Air-Water-Sand Mixtures

Simulating the dynamic, multiscale interactions between granular materials and multiphase fluids remains a significant computational challenge in computer graphics, as the visual complexity of such mixtures arises from strongly coupled small-scale structures. We present a novel, physically-based simulation framework for sand-water-air mixtures that couples a Lattice Boltzmann Method (LBM) for weakly-compressible two-phase fluids with a Material Point Method (MPM) for granular sand. Our approach is built upon a unified continuum formulation that expresses the governing equations for both fluid phases (air and water) and the granular medium within a consistent framework. To accurately capture the transition of sand from a dry, friction-dominated state to a soaked, sticky medium, we introduce a water retention model that describes how liquid infiltrates and is retained within the granular structure. Furthermore, we enforce volume conservation of the fluids within the mixture, ensuring numerical stability and physical realism. Our robust coupling mechanism enables the simulation of complex phenomena such as sand mobilization, transport, settling, and erosion across a wide range of density ratios. We demonstrate the efficiency of our method through several challenging scenarios, including the breaching of sand-walled basins, sediment-laden flows, and the erosive collapse of sand structures.