Research Associate: V. Sarin
Graduate Student: M. Knepley
Sponsors: NSF Grand Challenge, KDI
Simulations of solid-liquid flows are of great interest to numerous industries using sedimenting and fluidized suspensions, lubricated transport, and hydraulic fracturing of hydrocarbon reservoirs. The state-of-the-art preconditioners and iterative methods are unable to solve the ill-conditioned, large, sparse linear systems that arise in 3D simulations. We have proposed a novel multilevel approach that is a robust and effective preconditioner for these systems in addition to being efficiently parallelizable. Using this preconditioner, flows with thousands of particles can now be simulated on parallel computers such as the SGI Origin2000. Such simulations were not possible with existing methods. A unique feature of this approach is that a well-conditioned basis for the zero-divergence fluid space is explicitly computed. As a result, this technique is ideally suited for those engineering applications where conservation laws must be strictly enforced.
We plan to extend the multilevel approach to non-Newtonian fluid flows with larger number of particles. For such cases, issues related to visualization, data analysis, distributed object-oriented computing, and performance evaluation of software assume great importance - these will also be the focus of our continuing research.