A stable partitioned FSI algorithm for incompressible flow and structural shells

A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface conditions for the pressure and velocity in the fluid that are derived directly from the governing equations. The AMP scheme is stable even for very light structures, requires no sub-iterations, and can be made fully second-order, or higher-order, accurate. The new scheme is shown to be stable through the analysis of a model problem. Exact traveling wave solutions for three FSI model problems are derived. Numerical results for a linearized FSI problem in two-dimensions, using these exact solutions, demonstrate that the scheme is stable and accurate, even for very light structures.