A numerical framework for the direct simulation of solid-fluid systems

Abstract

Our understanding of solid-fluid dynamics has been severely limited by the nonexistence of a high-fidelity modeling capability for these multiphase systems. Continuum modeling approaches overlook the microscale solid-fluid interactions from which macroscopic system properties emerge, while experimental inquiries have been plagued by high costs and limited resolution. One promising numerical alternative is to simulate solid-fluid systems at the grain-scale, fully resolving the interaction of individual solid particles with other solid particles and the surrounding fluid. Until recently, the direct simulation of these systems has proven computationally intractable. In this thesis an accurate, efficient, and robust modeling capability for the direct simulation of solid-fluid systems is formulated and implemented. The coupled equations of motion governing both the fluid phase and the individual particles comprising the solid phase are solved using a highly efficient numerical scheme based on the discrete-element (DEM) and the lattice-Boltzmann (LB) methods. Particle forcing mechanisms represented in the model to at least the first order include dynamic fluid-induced forces, buoyancy forces, and intergranular forces from particle collisions, static formation stresses, and intergranular bonding. Coupling is realized with an immersed moving boundary scheme that has been thoroughly validated.

(cont.) For N solid bodies under simulation, the coupled DEM-LB numerical scheme scales roughly as O(N), and is highly parallelizable due to the local and explicit nature of the underlying algorithms. The coupled method has been implemented into a generalized modeling environment for the seamless definition, simulation, and analysis of two-dimensional solid-fluid physics. Extensive numerical testing of the model has demonstrated its accuracy and robustness over a wide range of dynamical regimes. Various fundamental phenomena have been reproduced in simulations, including drafting-kissing-tumbling interactions between settling particles, and the saltating transport regime of bed erosion.