Injae Lee

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.

A weak-coupling immersed boundary method for fluid–structure interaction with low density ratio of solid to fluid

Abstract We present a weak-coupling approach for fluid–structure interaction with low density ratio (ρ) of solid to fluid. For accurate and stable solutions, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid–structure interface at each time step, respectively. The incompressible Navier–Stokes equations, together with these provisional velocity and position at the fluid–structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid–structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate, respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 ( ρ min = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling.

A Discrete-Forcing Immersed Boundary Method for the Fluid-Structure Interaction of an Elastic Slender Body

In the present study, a new immersed boundary method for the simulation of flow around an elastic slender body is suggested. The present method is based on the discrete-forcing immersed boundary method by Kim et al. (J. Comput. Phys., 2001) and is fully coupled with the elastic slender body motion. The incompressible Navier-Stokes equations are solved in an Eulerian coordinate and the elastic slender body motion is described in a Lagrangian coordinate, respectively. The elastic slender body is modeled as a thin flexible beam and is segmented by finite number of blocks. Each block is then moved by the external and internal forces such as the hydrodynamic, tension, bending, and buoyancy forces. With the proposed method, we simulate several flow problems including flows over a flexible filament, an oscillating insect wing, and a flapping flag. We show that the present method does not impose any severe limitation on the size of computational time step. The results obtained agree very well with those from previous studies.Copyright