Computation of dynamic fluid-structure interaction in two-dimensional laminar flows using combined formulation

In fluid-structure interaction (FSI) problems, two different governing equations are solved together. In addition, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation which incorporates both the fluid and structure equations of motion into a single coupled variational equation. This does not necessitate the calculation of the fluid force on the surface of the structure explicitly when solving the equation of motion for the structure. A two-dimensional laminar channel flow divided by a plate and another two-dimensional laminar flow caused by the oscillation of a vertical plate in a cavity filled with a fluid are considered to investigate the dynamic FSI between the fluid and the plate. The Navier-Stokes equation modified with the arbitrary Lagrangian-Eulerian (ALE) technique is solved using a P2P1 Galerkin finite element method (FEM). The equation of motion for the plate is solved using a Galerkin FEM without considering the internal structural damping effect. Numerical results for steady channel flow are in good agreement with the existing work of Wang. In addition to the Reynolds number, two nondimensional parameters, which govern this fluid-structure system, are proposed. When the Reynolds number and the geometry are fixed, it is noted that the damping of the amplitude of plate oscillation increases as the dynamic viscosity and the density of the fluid increase, and that the added mass is linearly proportional to the fluid density but independent of fluid viscosity.