INTEGRAL EQUATIONS OF THE SECOND KIND FOR STOKES FLOW: DIRECT SOLUTION FOR PHYSICAL VARIABLES AND REMOVAL OF INHERENT ACCURACY LIMITATIONS

Abstract

Boundary integral methods offer the most attractive combination of generality and computational efficiency for a wide class of particulate Stokes flow problems. Integral equations of the first kind have been numerically applied for more than a decade, whereas those of the second kind are numerically better behaved but involve abstract nonphysical density distributions and have not gained much popularity in applications. We show how the latter may be used for the direct solution of mobility problems, and how the surface tractions corresponding to rigid body motion of a particle may be easily found, thus removing the major disadvantages of the second kind formulations. For the numerical examples we also show how Fourier analysis may be applied to non-axisymmetric problems with axisymmetric boundaries to yield one-dimensional Fredholm integral equations of the second kind. As an application we solve the resistance problem with a numerically efficient quadrature collocation method that avoids the complication...