An integral equation method for coupled fluid/fluid scattering in three dimensions

Abstract

In this article, the time-harmonic, three-dimensional fluid/fluid scattering problem is reformulated using an integral equation method. In this method, the fluid/fluid boundary value problem leads to a pair of boundary integral equations, one for the exterior fluid medium and the other for the interior fluid medium. The two integral equations are coupled by the continuity relationships at the interface between the two media. The coupled integral equations are reduced to algebraic equations by using a quadratic isoparametric representation for the geometry and variables of the problem. As an example, the scattering of a plane sound wave by an air bubble in water is studied. Of special interest here is the ability of the integral equation method to predict accurately the giant monopole resonance of the bubble. A half-space, fluid/fluid scattering problem is formulated using modified kernels in the basic integral equations. The use of the half-space formulation is illustrated for the scattering of a plane sound wave by an air bubble in water and in proximity to a hard wall.