Application of the Singularity Method for a Single Rigid or Fluid Particle

Abstract

The linearity of the creeping flow equations allows the creation of a class of solution methods that is readily applied to various type of hydrodynamic problems. Solutions of problems involving applications of internal concentrated forces are of fundamental interest for fluid mechanics Apart from being Green’s functions, these fundamental solutions can be used in constructing the new solutions of more complicated and physically realizable problems. The construction of such solutions is known as a singularity method. This method is employed not only for obtaining solutions which are not known so far, but also to recover already known solutions in a very simple fashion. If the boundary shapes of the problem under consideration are simple, then the analytical solution can be achieved via the internal distributions of force and force multipole singularities. Unfortunately, a systematic procedure for choosing the singularities necessary to solve any particular problem does not exist yet. One relies on a combination of intuition and a knowledge of the properties of the basic singularities to make an appropriate guess. It is clear that suggestions about the symmetry of the considered flow have an important significance.