Shallow Sand Equations: Real-Time Height Field Simulation of Dry Granular Flows

Kuixin Zhu, Xiaowei He, Sheng Li, Hongan Wang, Guoping Wang

Granular media is the second-most-manipulated substance on Earth, second only to water. However, simulation of granularmedia is still challenging due to the complexity of granular materials and the large number of discrete solid particles. As we know, drygranular materials could form a hybrid state between a fluid and a solid, therefore we propose a two-layer model and divide thesimulation domain into a dilute layer, where granules can move freely as a fluid, and a dense layer, where granules act more like asolid. Motivated by the shallow water equations, we derive a set of shallow sand equations for modeling dry granular flows bydepth-integrating three-dimensional governing equations along its vertical direction. Unlike previous methods for simulating a 2Dgranular media, our model does not restrict the depth of the granular media to be shallow anymore. To allow efficient fluid-solidinteractions, we also present a ray casting algorithm for one-way solid-fluid coupling. Finally, we introduce a particle-tracking method toimprove the visual representation. Our method can be efficiently implemented based on a height field and is fully compatible withmodern GPUs, therefore allows us to simulate large-scale dry granular flows in real time.

Shallow Sand Equations: Real-Time Height Field Simulation of Dry Granular Flows