Null-field boundary integral equation approach for hydrodynamic scattering by multiple circular and elliptical cylinders

Abstract

In this paper, the null-field boundary integral formulation in conjunction with the degenerate kernel and the Mathieu function in the elliptic coordinates is proposed to solve the hydrodynamic scattering problem by multiple circular and elliptical cylinders. Based on the adaptive observer system, the present method can solve the water wave problem containing circular and elliptical cylinders at the same time in a semi-analytical manner. The closed-form fundamental solution is expressed in terms of the degenerate kernel in the polar and elliptic coordinates for circular and elliptical cylinders, respectively. Several examples are demonstrated to see the validity of the semi-analytical approach.