A partitioned numerical scheme for fluid-structure interaction with slip
We present a loosely coupled, partitioned scheme for fluid-structure interaction problems with the Navier slip boundary condition. The fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid, interacting with a thin elastic structure modeled by the membrane or Koiter shell type equations. The fluid and structure are coupled via two sets of coupling conditions: a dynamic coupling condition describing balance of forces, and a kinematic coupling condition describing fluid slipping tangentially to the moving fluid-structure interface, with no penetration in the normal direction. We propose a novel, efficient partitioned scheme where the fluid sub-problem is solved separately from the structure sub-problem, and there is no need for sub-iterations to achieve stability, convergence, and its optimal, first-order accuracy. We derive energy estimates, which prove that the proposed scheme is unconditionally stable, and present convergence analysis which shows that the method is first-order accurate in time and optimally convergent in space. The theoretical rates of convergence in time are confirmed numerically on an example with an explicit solution using the method of manufactured solutions. The effects of the slip rate and fluid viscosity on the FSI solution are numerically investigated in two additional examples.