Proceedings of ASME-JSME-KSME Joint Fluids Engineering Conference 2011 AJK2011-FED July 24-29, 2011, Hamamatsu, Shizuoka, JAPAN AJK2011-20006 AN IMPROVED PENALTY IMMERSED BOUNDARY METHOD FOR FLUID-FLEXIBLE BODY INTERACTION Wei-Xi Huang * Department of Mechanical Engineering, KAIST Daejeon, Korea Cheong Bong Chang Department of Mechanical Engineering, KAIST Daejeon, Korea Hyung Jin Sung Department of Mechanical Engineering, KAIST Daejeon, Korea * Also at Department of Engineering Mechanics, Tsinghua University, Beijing, China ABSTRACT An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid-flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, three-dimensional simulations of fluid-flexible body interaction are carried out, including deformation of a spherical capsule in a linear shear flow. A comparison between the numerical results and the theoretical solutions is presented. INTRODUCTION Since the seventies of the last century, the immersed boundary (IB) method has gained more and more popularity due to its ability in simulating complex flows and has been applied to various engineering flow problems [1]. The basic idea of the IB method is to avoid the necessity of adopting body-fitted meshes by adding a momentum forcing in the equations of motion to mimic complex boundaries. In this way, a flow over fixed or moving boundaries can be simulated on fixed Eulerian meshes, thus significantly simplifying the solution process. The original IB method was proposed by Peskin [2]. Starting from the continuum mechanics point of view, Peskin [3] wrote the momentum equations of an incompressible elastic material in the same form as those of the incompressible fluid, i.e. the Navier-Stokes (N-S) equations. This is especially efficient for dealing with a massless (or neutrally buoyant) elastic body immersed in fluid. In order to simulate a massive elastic body moving in fluid, Zhu and Peskin [4] spread the solid mass to the near Eulerian grid points in the same manner as the elastic force. The multigrid method was used to solve the discretized N-S equations with a variable density coefficient, instead of the efficient FFT method. Furthermore, Kim and Peskin [5] proposed an improved method referred to as the penalty IB (pIB) method, where the solid mass is added by introducing a virtual boundary with the needed mass that does not directly interact with the fluid but rather is connected by a stiff spring to its twin massless boundary that moves with the local fluid velocity. In this way, they were able to solve the N-S equations with a constant density coefficient, and thus retain the use of the FFT method. In the present study, our objective is to establish an efficient numerical algorithm for simulating fluid-flexible interaction. For general consideration, the fluid solver and the solid solver are developed separately. The incompressible fluid motion is defined on the Eulerian domain and is solved by the fractional step method on a staggered Cartesian grid system. The solid motion is described by the Lagrangian variables and is solved