An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid

Abstract

This paper introduces a second kind boundary integral equation which can be used to model the motion of a single gas or vapour bubble in a liquid. In the special case of a sphere, the eigenvalues of the underlying integral operator are used to show that the new second kind formulation has much more desirable spectral properties than the more usual first kind integral equation formulation which has often been used in practice. Further, the numerical results presented in this paper show that the new scheme yields reasonably accurate results even with a coarse mesh.