Benjamin Koger Cook

A direct simulation method for particle‐fluid systems

A coupled numerical method for the direct simulation of particle‐fluid systems is formulated and implemented. The Navier‐Stokes equations governing fluid flow are solved using the lattice Boltzmann method, while the equations of motion governing particles are solved with the discrete element method. Particle‐fluid coupling is realized through an immersed moving boundary condition. Particle forcing mechanisms represented in the model to at least the first‐order include static and dynamic fluid‐induced forces, and intergranular forces including particle collisions, static contacts, and cementation. The coupling scheme is validated through a comparison of simulation results with the analytical solution of cylindrical Couette flow. Simulation results for the fluid‐induced erosive failure of a cemented particulate constriction are presented to demonstrate the capability of the method.

Contact resolution algorithm for an ellipsoid approximation for discrete element modeling

The efficiency of a discrete element implementation relies on several factors, including the particle representation, neighbor‐sorting algorithm, contact resolution, and force generation. The focus of this paper is on the four‐arc approximation for an ellipsoid – a geometrical representation useful in simulations of large numbers of smoothly shaped particles. A new contact resolution algorithm based on the four‐arc approximation is presented, which takes advantage of the properties of the geometry to provide favorable empirical convergence properties compared with the method proposed earlier. Special attention is given to the software implementation of the algorithm, and a discussion of the computational efficiency of the algorithm is provided.

On the application of quaternion‐based approaches in discrete element methods

Purpose – Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are non‐trivial. Many molecular dynamics and non‐deformable discrete element applications employ an explicit integration for resolving orientation, often involving products of matrices, which have well‐known drawbacks. The purpose of this paper is to investigate commonly used algorithms for resolving rotational motion and describe the application of quaternion‐based approaches to discrete element method simulations.Design/methodology/approach – Existing algorithms are compared against a quaternion‐based reparameterization of both the central difference algorithm and the approach of Munjiza et al. for finite/discrete element modeling (FEM/DEM) applications for the case of torque‐free precession.Findings – The resultant algorithms provide not only guaranteed orthonormality of the resulting rotation but also allow assumptions of small‐angle ...

A Coupled DEM-LB Model for the Simulation of Particle-Fluid Systems

Our understanding of particle-fluid dynamics has been severely limited by the nonexistence of a high-fidelity modeling capability. Continuum modeling approaches overlook the microscale particle-fluid interactions from which macroscopic system properties emerge, while experimental inquiries are plagued by high costs and limited resolution. One promising numerical alternative is to simulate particle-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 research, a robust modeling capability for the direct simulation of particle-fluid systems has been 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 static and dynamic fluid-induced forces, and intergranular forces from particle collisions, static contacts, and cementation. The coupled method has been implemented into a generalized modeling environment for the seamless definition, simulation, and analysis of two-dimensional particle-fluid physics. Extensive numerical testing of the model has demonstrated its accuracy over a wide range of dynamical regimes.