Simon Fraser University
Burnaby, British Columbia, Canada
Integral equation methods for computing the hydrodynamic interactions among solid particles suspended in a slow, viscous fluid are presented. The particle boundaries may have arbitrary shape and they may be suspended in an unbounded or wall-bounded fluid. The analytic formulation of the integral equation is based on complex variables, and the Fast Multipole-based iterative solution procedure requires only $O(N)$ operations, where $N$ is the number of nodes in the discretization of the boundary. Thus, large-scale problems with complex geometry can be solved using modest computational resources. >From the hydrodynamic interactions, the particle motions are determined either by computing a sequence of steady-state Stokes flow problems or by including the weak effects of the particles' inertia. Examples will include the sedimentation of particles in a quiescent fluid and the motion of particles in a shear flow. Methods for computing the time evolution of bubbles in a Stokes flow will also be discussed, as will extensions to three dimensions.