Asymptotic solution of 2D and 3D boundary integral equations arising in Fluid Mechanics and Electrostatics

Abstract

We present a systematic method to asymptotically expand, with respect to a small slenderness or thickness parameter, the solution of a wide class of boundary integral equations arising in Electrostatics and Fluid Mechanics. The adopted point of view permits us to bypass the tedious matching rules of the widely employed method of matched asymptotic expansions. If each step of the proposed procedure is described within a general framework, the paper also addresses applications to 2D and 3D problems. The 3D example not only briefly reports but also extends the results obtained elsewhere by the author. The whole 2D application to the potential flow around a thin aifoil is original. Finally, a special attention is paid to the case of a non-smooth 2D domain.