Chapter 5 Boundary Integral Approaches

Abstract

Publisher Summary This chapter discusses the boundary integral approaches. It deals with a particular set of FSI problems involving a rigid or linear elastic body interacting with potential flow, acoustic medium, or low Reynolds number flow. The commonality of these FSI problems is the boundary integral formulations of the unknown function and its derivatives, which often warrant exact or analytical solutions. If, however, the shape of the geometrical domain physically occupied by the coupled media precludes analytical solutions, boundary element methods must be used to solve these integral formulations. It begins with a separate presentation of underlying physics and problem formulations for potential flow, acoustic medium, and low Reynolds number flow. It discusses the fundamental concepts of Green's functions, boundary integral formulations, and the corresponding boundary element methods. The radiation and scattering of waves are presented with respect to potential flows. Potential flow is often called ideal flow, where the bulk of the fluid is assumed to be incompressible and in viscid.