Modeling of Dynamic Rock–Fluid Interaction Using Coupled 3-D Discrete Element and Lattice Boltzmann Methods
Scour of rock is a challenging and interesting problem that combines rock mechanics and hydraulics of turbulent flow. On a practical level, rock erosion is a critical issue facing many of the world’s dams at which excessive scour of the dam foundation or spillway can compromise the stability of the dam resulting in significant remediation costs, if not direct personal property damage or even loss of life. This interaction between the blocky rock mass and water is analyzed by directly modeling the solid and fluid phases—the individual polyhedral blocks are modeled using the discrete element method (DEM) while water is modeled using the lattice Boltzmann method (LBM). The LBM mesh is entirely independent of the DEM discretization, making it possible to refine the LBM mesh such that transient and varied fluid pressures acting on the rock surfaces are directly modeled. This provides the capability to investigate the effect of water pressure inside the fractured rock mass, along potential sliding planes, and can be extended to rock falls and slides into standing bodies of water such as lakes and reservoirs. Results show that the coupled DEM–LBM implementation is able to accurately capture the interaction between polyhedral rock blocks and fluid by analytically solving for the solid volume fraction in the coupling computations using convex optimization and simplex integration; however, further performance improvements are necessary to simulate realistic, field-scale problems. Particularly, adaptive mesh refinement and multigrid methods implemented in a parallel computing environment will be essential for capturing the highly computationally intensive and multiscale nature of rock–fluid interaction.
Keywords: Rock scour, Fluid–solid interaction, Discrete element method, Lattice Boltzmann method, Linear programming, Simplex integration