Galerkin boundary integral formulation for axisymmetric stokes flow

A Galerkin boundary integral formulation for 3D axisymmetric Stokes flow is presented. The singular integrals are evaluated by splitting the complicated Green's function kernels into a singular term that can be integrated analytically, plus a term for which Gauss quadrature provides sufficient accuracy. As in a previous axisymmetric Laplace implementation, the treatment of the additional on-axis singularity is aided by employing a modified Galerkin weight function, and a similar splitting method is then employed to handle this singularity. The target application of the Stokes algorithm is to model the breakup of one viscous fluid enclosed inside a second, and this two fluid problem can be formulated in terms of a single boundary integral equation along the interface. The Galerkin form for this equation is derived herein.