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.

翻译：模拟流体-颗粒流动对于理解自然灾害、工业过程以及计算机图形学中视觉真实的现象至关重要。由于连续流体与离散颗粒介质之间存在强非线性耦合，这些系统难以模拟，在大规模条件下同时实现物理保真度和计算效率具有挑战性。本研究提出了一个大规模流体-颗粒模拟的统一框架，将用于流体的格子玻尔兹曼方法（LBM）与用于沙、雪等颗粒材料的物质点法（MPM）相耦合。我们引入了一种基于实体几何结构的自适应分块多级HOME-LBM求解器，能够在多种格子分辨率下实现高效的内存使用和计算性能。通过矩量的一致重标度定律，可在细化界面间准确传递宏观物理量；同时，基于GPU的算法能根据粒子运动动态维护多级分块结构。通过强制所有MPM粒子位于最精细的流体节点内，我们实现了流体与颗粒相之间的精确双向耦合。本框架支持雪崩、沙尘暴和沙粒迁移等多种大规模现象，展现出高物理保真度与计算效率。