A DLM/FD method for fluid/flexiblebody interactions
Abstract
In this study, we extended the distributedLagrangemultiplier/fictitiousdomain (DLM/FD) formulation of Glowinski et al. [Int. J. Multiphase Flow 25 (1999) 755] for the fluid/rigidbody interactions to deal with the fluid/flexiblebody interactions by replacing Newton's equations of motion for the rigid body with the continuum equations for the general solid material. Similar to the rigidbody case where the DLM is introduced as a pseudo body force to enforce the constraint of rigidbody motion of the fictitious fluid in the solid domain, the Lagrange multiplier in our formulation is to enforce the fictitious fluid to move at the same velocity as the solid. For our computational scheme, a firstorder accurate fractional step scheme is employed to decouple the entire system into three subsystems: a fluid problem, a solid problem and a Lagrange multiplier problem; the flow problem is solved with the projection method on halfstaggered grids; the solid problem is solved with the Lagrangian finite element method and the Newton iterative method; and the incompressibility of the material is implemented with the penalty function method. The proposed method is applied to two typical fluidstructure interaction problems: the flowdriven oscillation of a flexible plate along the flow direction and the selfsustained oscillation across the flow direction. Both results compare favorably with previously reported numerical and experimental results, and show that our method is suited to the simulation of the motion of an incompressible nonlinear elastic material in a fluid.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 2005
 DOI:
 10.1016/j.jcp.2004.12.026
 Bibcode:
 2005JCoPh.207....1Y