The boundary element method applied to the creeping motion of a sphere

The boundary element method is employed to describe the motion of a sphere at low Re in a viscous, incompressible fluid. A one-dimensional grid of nodes represents the semicircular meridian of the sphere during the creeping flow. Equations of motion and mass conservation for an incompressible fluid are defined in tensor form and the Galerkin procedure is applied to a set of velocity, pressure, and stress fields. Kernel functions are formulated in terms of complete elliptic integral equations of the first and second kind. Boundary discretization is effected by utilizing geometrically linear elements with constant velocity and traction values, with each element associated with one central node. The pressure field is expressed in rectangular coordinates to simplify the kernels. Improvements in accuracy are indicated by using increasing numbers of elements.