9527123 Joseph This project will develop highly efficient methods for computing the three-dimensional motion of large number of particles in solid-liquid flows, under the action of the hydrodynamic forces and torques exerted by the suspending fluid, and use these methods to elucidate the fundamental dynamics of particulate flows and solve problems of engineering interest. The goal is to develop high-performance, state-of -the-art software packages called particle movers, capable of simulating the motion of thousands of particles in 2-D and hundreds in 3-D domains, in both Newtonian fluids, governed by the Navier-Strokes equations, and in several popular models of viscoelastic fluids. Such simulations will be extremely computationally intensive. It is therefor imperative to develop the most efficient possible computational schemes, and to implement them on parallel machines, using state-of-the-art parallel algorithms. The project will develop two different computational schemes for simulating solid-liquid flows on parallel computers. The first is a generalization of the standard Galerkin finite element method in which both the fluid and particle equations of motion are incorporated into a single variational equation, containing both fluid and particle velocities as primitive unknowns. In the second approach, an embedding method, the fluid flow is computed as if the space occupied by the particles were filled with fluid. The no-slip boundary condition of the particle boundaries is enforced as a constraint using Lagrange multipliers. This allows a fixed grid to be used, eliminating the need for remeshing, a definite advantage in parallel implementations. The new schemes will be used to study the microstructural (pair interaction) effects which produce clusters and anisotropic structures in particulate flows, to produce statistical analyses of particulate flows (mean values, fluctuation levels and spectral properties), to derive engineering correlations of the kind usually obtained from expe riments, and to provide clues and closure data for the development of two-phase flow models and a standard against which to judge the performance of such models. They will also be used to solve practical problems of industrial interest such as sedimentation, fluidization an slurry transport of solid particles in Newtonian and viscoelastic fluids.
