Adaptive GPU Kinetic Solver for Fluid-Granular Flows

Abstract

Simulating fluid-granular flows is crucial for understanding natural disasters, industrial processes, and visually realistic phenomena in computer graphics. These systems are challenging to simulate because of the strong nonlinear coupling between continuum fluids and discrete granular media, making it difficult to achieve both physical fidelity and computational efficiency at large scales. In this work, we present a unified framework for large-scale fluid-granular simulation that couples the Lattice Boltzmann Method (LBM) for fluids with the Material Point Method (MPM) for granular materials such as sand and snow. We introduce an adaptive block-based multi-level HOME-LBM solver based on solid geometric structures, enabling efficient memory usage and computational performance across multiple lattice resolutions. Consistent rescaling laws for moments allow accurate transfer of macroscopic quantities across refinement interfaces, while a GPU-based algorithm dynamically maintains the multi-level blocks in response to particle motion. By enforcing that all MPM particles reside within the finest fluid nodes, we achieve accurate two-way coupling between fluid and granular phases. Our framework supports a wide range of large-scale phenomena, including snow avalanches, sandstorms, and sand migration, demonstrating high physical fidelity and computational efficiency.

Figures (10)

• Figure 1: Multi-level block structure in 2D. Yellow denotes sand particles. Red, blue, and green denote different levels.
• Figure 2: Blue/green arrows and areas denote downward/upward transfer and interface areas $\mathcal{I}^d_{\bullet}$/$\mathcal{I}^u_{\bullet}$, respectively. Black circles indicate corresponding children who transfer macroscopic quantities to their parents during the upward transfer.
• Figure 3: SC, S, and C denote the streaming–collision, streaming-only, and collision-only steps in the LBM advance, respectively. Ex indicates force exchange between LBM and MPM. G, P2G, and G2P denote grid update, particle-to-grid, and grid-to-particle operations in the MPM integration. Blue and green denote downward and upward transfers between LBM levels, respectively.
• Figure 4: Powder Snow. The powder snow cloud is generated with the advance of a bulk of snow pack. The entrainment rates from top to bottom are 1e-7, 4.5e-6, and 1e-6, respectively. A denser powder-snow cloud is less turbulent in our simulation.
• Figure 5: 2D Avalanche on a slope. A high-fidelity powder snow avalanche simulation descending a curved slope. Typical phenomena, including aerodynamic entrainment, vortex shedding, and the turbulent suspension cloud driven by Kelvin-Helmholtz instability, are reproduced.