Direct Numerical Simulation of Liquid-Solid Flow

D. Joseph and Y. Saad, University of Minnesota
R. Glowinski, University of Houston
H. Hu, University of Pennsylvania
A. Sameh, Purdue University

Research Objectives

Sponsored by a National Science Foundation Grand Challenge high performance computing grant, the DOE Office of Basic Energy Sciences, and several industrial partners (Dowell-Schlumberger, Schlumberger, Shell, Stimlab, and Intevep, S.A.), we seek to develop state-of-the-art software packages that solve initial-value problems for dispersion of thousands of particles on parallel computers. To achieve this, a marriage between computational fluid dynamics (CFD) and computer science (CS) is created to produce the most efficient parallel preconditioners and iterative schemes. These are needed to handle the large, time-consuming nonlinear and linear algebraic equations that arise in this investigation.

Computational Approach

In this project, particles are moved by Newton's laws under the action of hydrodynamic forces computed from the numerical solution of the fluid equations. Solutions of the initial value problem for dispersion of solid particles in fluidized beds and slurries, sand placement in fracture oil reservoirs, cleaning of drill cuttings from oil wells, and other applications are solved without approximations beyond those inherent in simulations.

The two parallel software packages developed in this project use a new, combined weak formation. In this formation, the fluid and particle equations of motion are combined into a single, weak equation of motion from which hydrodynamic forces and torques on the particles have been eliminated. These and other results achieved in this Grand Challenge project have opened new and promising lines for investigation.

Accomplishments

The collaboration of CFD and CS communities, which traditionally speak different languages, has given rise to an interdisciplinary group that communicates with ease across disciplinary boundaries. This interdisciplinary research effort has already resulted in two state-of-the-art parallel software packages. The first, which uses a moving unstructured body-fitted grid, is the only numerical package anywhere that can move solid particles in a viscoelastic fluid in direct simulation. The second is an elegant package that uses a fixed grid in which particles are represented by a field of Lagrange multipliers associated with the constraint of rigid body motion. The fixed-structured grid offers opportunities for using rapid solvers that are ideally suited for parallel implementation.

Significance

Performance results obtained on two parallel computational platforms, an SGI Origin 2000 and a Cray T3E, indicate that routine fine-tuning of various kernels results in efficient utilization of the parallelism offered by these architectures. A future aim is to produce industrial-strength counterparts of the codes that are portable across a variety of parallel architectures.

1,109 particles flowing in a Newtonian fluid in a channel. The mixture is pumped upwards against gravity. The color shows the stream function.

Publications

P. Y. Huang, J. Feng, H. H. Hu, and D. D. Joseph, "Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids," Journal of Fluid Mechanics 343,73-94 (1997).

P. Y. Huang, H. H. Hu, and D. D. Joseph, "Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids," Journal of Fluid Mechanics 362,297-325 (1998).

http://www.aem.umn.edu/Solid-Liquid_Flows