INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.2731 Simulation of flow-flexible body interactions with large deformation Emad Uddin and Hyung Jin Sung * ,† Department of Mechanical Engineering,KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea SUMMARY A modified front-tracking method was proposed for the simulation of fluid-flexible body interactions with large deformations. A large deformable body was modeled by restructuring the body using a grid adaptation. Discontinuities in the viscosity at the fluid-structure interface were incorporated by distributing the viscosity across the interface using an indicator function. A viscosity gradient field was created near the interface, and a smooth transition occurred between the structure and the fluid. The fluid motion was defined on the Eulerian domain and was solved using the fractional step method on a staggered Cartesian grid system. The solid motion was described by Lagrangian variables and was solved by the finite element method on an unstructured triangular mesh. The fluid motion and the structure motion were independently solved, and their interaction force was calculated using a feedback law. The interaction force was the restoring force of a stiff spring with damping, and spread from the Lagrangian coordinates to the Eulerian grid by a smoothed approximation of the Dirac delta function. In the numerical simulations, we validated the effect of the grid adaptation on the solid solver using a vibrating circular ring. The effects of the viscosity gradient field were verified by solving the deformation of a circular disk in a linear shear flow, including an elastic ring moving through a channel with constriction, deformation of a suspended catenary, and a swimming jellyfish. A com- parison of the numerical results with the theoretical solutions was presented. Copyright © 2011 John Wiley & Sons, Ltd. Received 20 May 2011; Revised 28 September 2011; Accepted 29 October 2011 KEY WORDS: immersed boundary method; front-tracking method; flexible body; fluid-structure interac- tion; grid adaptation; indicator function 1. INTRODUCTION Systems in which a viscous fluid interacts with a large deformable boundary are of considerable interest in the study of fluids. Important engineering applications of large deformable bodies include cellular biology and drug delivery, and such biological systems that interact with fluids, such as the human heart in the presence of blood flow, insect flight, aquatic animal locomotion, filament flap- ping dynamics, blood cell aggregation, biofilm processing, and parachute dynamics, are amenable to simulation [1]. Simulations of systems in which flexible bodies interact with the surrounding fluid must account for both the fluid and structure dynamics [2]. It is because the body is highly deformable, the resolution of some parts of the structure may become inadequate, whereas the res- olution of other parts may be unnecessarily fine as a result of crowding with structural elements. Discontinuities in the fluid properties across the interface may also be present. Various forms and extensions of numerical methods have been developed for simulating fluid- structure interaction problems. Two of the most promising methods are the immersed boundary (IB) method [3] and the front-tracking method [4]. In the IB method, the momentum equations of an *Correspondence to: Hyung Jin Sung, Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea. † E-mail: hjsung@kaist.ac.kr Copyright © 2011 John Wiley & Sons, Ltd.