DOE ACTS COLLECTION Workshop Robust and High Performance Tools for Scientific Computing September 4-7, 2002

Preconditioned iterative solvers for linear systems, multi-level method in Poisson solver, level-set method, and to implement them on parallel architectures efficiently.

We are developing our scalable and highly efficient parallel finite-element codes for the direct numerical simulation of the 2-D and 3-D motion of large number of solid particles in Newtonian and viscoelastic fluids. We have developed two separate codes (ALE and DLM particle movers). The ALE particle mover is based on a generalization of the standard Galerkin finite-element method that uses an unstructured mesh and an ALE scheme to handle the time-dependent domain. The DLM particle mover is based on a fictitious-domain method, in which the fluid flow equations are enforced both inside and outside the particle boundaries. Both methods use a combined fluid-particle weak formulation from which the hydrodynamic forces and torques have been eliminated.

We will continue our efforts to improve the performance of our particle movers by paralleling the code for 3-D motion, and will continue our computational investigations into the fundamental dynamics of fluid-particle motions. At present we are working on correlations for lift force in Poiseuille flow. Studies of the lift of particles in 3-D flow are underway.

We also plan to use numerical simulation to investigate particle motions in fluid interfaces. In our finite element code the level-set method is used to track the interface position and the distributed Lagrange multiplier method is used to track the motion of rigid particles. Progress has already been made in simulating the attraction of two particles trapped in a two-fluid interface.