Integral equation methods for particle simulations in creeping flows

Integral equation methods for computing the hydrodynamic interactions among solid particles suspended in a creeping flow are presented. The particles 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 solve 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 coupling the particlesʹ equation of motion thereby including the weak effects of the particlesʹ solid inertia. Examples will include the sedimentation of particles in a quiescent fluid towards or parallel to a plane wall and the motion of neutrally-buoyant particles in a shear flow.