Calculation of Axisymmetric Stokes Flow Past a Particle

The singularity of the elliptic integral in the boundary integral equations governing the axisymmetric Stokes flow past a particle is reduced to a logarithmic singularity and the reduced integrals are calculated by the derived four point Gaussian quadrature with a weighted function containing logarithmic singularity, which makes the calculation of the singular integrals succinct, universal and highly accurate. the method proposed can be used to calculate axisymmetric Stokes flow past a particle with arbitrarily convex or concave profile. The numerical solution for the Stokes flow past a sphere are coincident with the exact solution. For the Stokes flow past a particle with a concave profile, convergent and reasonable numerical solutions are obtained.