Fluid-structure interaction: the immersed boundary method

Abstract

The immersed boundary method (IBM) is presented in this chapter. Its important task is to provide the bidirectional coupling between the fluid motion and the membrane dynamics. The basic idea of this coupling is that the membranes move along with the ambient fluid (no-slip condition at the interface) and that any force acting on the membranes also acts on the fluid and vice versa (Newton’s third law). After an overview in section 6.1, the governing equations are motivated in section 6.2. The discretization of the IBM equations is discussed in section 6.3, followed by an alternative motivation of these equations based on statistical physics in section 6.4.