Simulation of flexible filaments in a uniform flow by the immersed boundary method Wei-Xi Huang, Soo Jai Shin, Hyung Jin Sung * Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea Received 19 February 2007; received in revised form 27 June 2007; accepted 4 July 2007 Available online 21 July 2007 Abstract An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow. The proposed IB method is based on an efficient Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. The fluid motion defined on an Eulerian grid and the filament motion defined on a Lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law. A direct numerical method is developed to calculate the filament motion under the constraint of inextensibility. When applied to the case of a swinging filament analogous to a rope pendulum, the proposed method gave results very similar to those of the analytical solution derived using the perturbation method. For a flexible filament flapping in a uniform flow, the mecha- nism by which small vortex processions are produced was investigated. The bistable property of the system was observed by altering the filament length, and the effects of the boundary condition at the fixed end (simply supported or clamped) were studied. For two side-by-side filaments in a uniform flow, both in-phase flapping and out-of-phase flapping were reproduced in the present simulations. A repulsive force was included in the formulation to handle collisions between the free ends of side-by-side filaments undergoing out-of-phase flapping. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Immersed boundary method; Fluid-structure interaction; Flexible filament; Inextensibility; Feedback forcing 1. Introduction Systems involving flexible bodies interacting with a surrounding fluid flow are commonplace – for example flapping flags and swimming fishes – and are becoming increasingly prevalent in biological engineering appli- cations. Such phenomena are challenging to model numerically on account of their complex geometries and freely moving boundaries, which give rise to complicated fluid dynamics. In these systems, the flexible body acts on the surrounding fluid, forcing it to move with the moving boundary. On the other hand, the fluid exerts forces on the flexible body through pressure differences and viscous shear stresses. Together, these interactions 0021-9991/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2007.07.002 * Corresponding author. Tel.: +82 42 869 3027; fax: +82 42 869 5027. E-mail address: hjsung@kaist.ac.kr (H.J. Sung). Journal of Computational Physics 226 (2007) 2206–2228 www.elsevier.com/locate/jcp