Application of the Singularity Method for Unsteady Flows Past Rigid or Fluid Particles

Abstract

The singularity method for the computation of unsteady viscous flows involving rigid or fluid particles was developed by direct analogy with the application of the same method for the corresponding problems of steady Stokes flows. This has been done by Williams (1966), Kanwal (1971), Kim and Russel (1985), Pozrikidis (1989a) and many others. As in the steady case the basic idea is to represent the flow in terms of discrete or continuous distributions of fundamental solutions to the governing unsteady Stokes equations. Depending on the nature of the flow and the geometry of the particles, the type of fundamental solutions is determined. Approximate solutions for slender particles can be obtained by using a line distribution of fundamental solutions along a properly defined particle axis. In order to account for inter-particle or particle-boundary interactions, it is convenient to combine the singularity method with the method of reflections (Kim and Russel, 1985).