Title: Evaluation of near-singular integrals with application to vortex sheet and Stokes flow

Abstract: Boundary integral formulations yield efficient numerical methods to solve elliptic boundary value problems. They are the method of choice for interfacial fluid flow, either in the inviscid vortex sheet limit, or the viscous Stokes limit. The fluid velocity at a target point is given by integrals over the interfaces. However, for target points near, but not on the interface, the integrals are near singular and standard quadratures lose accuracy. While several accurate methods exist to resolve the analytic integrals that appear in planar geometries, they dont generally apply to the non-analytic case that arises in axisymmetric geometries. Motivated by the latter, we developed a simple method that accurately resolves a large class of integrals. This talk describes the method, presents analytical convergence results, and applies it to resolve planar vortex sheet and axisymmetric Stokes flow.