A complementary study of analytical and computational fluid-structure interaction

This paper introduces new initial value problems for the design and analysis of fluid-structure interaction algorithms. The problems are constructed from a finite number of sinusoidal perturbations of thin structures superposed on incompressible fluids. Explicit analytical solutions are provided for rigorous quantitative comparisons including viscous effects. The equation governing a single inviscid mode is split into fluid and structure subproblems and numerical parameters are derived for several partitioned algorithms based on a Dirichlet-Neumann decomposition and a second-order backward difference time discretization. Numerical experiments are performed using a stabilized fractional-step finite element method for the fluid and membrane finite elements for the structure. The convergence behaviour of the finite element solutions to the analytical solutions is demonstrated. Finally, the stability and performance of the numerical parameters derived from a single inviscid mode are presented for more general problems including multiple modes and viscous effects.