A discrete-forcing immersed boundary method for the fluid-structure interaction of an elastic slender body

We present an immersed boundary (IB) method for the simulation of flow around an elastic slender body. The present method is based on the discrete-forcing IB method for a stationary, rigid body proposed by Kim, Kim and Choi (2001) [25]. The discrete-forcing approach is used to relieve the limitation on the computational time step size. The incompressible Navier-Stokes equations are implicitly coupled with the dynamic equation for an elastic slender body motion. The first is solved in the Eulerian coordinate and the latter is described in the Lagrangian coordinate. The elastic slender body is modeled as a thin and flexible solid and is segmented by finite number of thin blocks. Each block is moved by external and internal forces such as the hydrodynamic, elastic and buoyancy forces, where the hydrodynamic force is obtained directly from the discrete forcing used in the IB method. All the spatial derivative terms are discretized with the second-order central difference scheme. The present method is applied to three different fluid-structure interaction problems: flows around a flexible filament, a flapping flag in a free stream, and a flexible flapping wing in normal hovering, respectively. Computations are performed at maximum CFL numbers of 0.75-1. The results obtained agree very well with those from previous studies.