A partitioned numerical scheme for fluid–structure interaction with slip

We present a loosely coupled, partitioned scheme for solving fluid–structure interaction (FSI) problems with the Navier slip boundary condition. The fluid flow is modeled by Navier–Stokes equations an incompressible, viscous fluid, interacting thin elastic structure membrane or Koiter shell type equations. and are coupled via two sets of coupling conditions: dynamic condition describing balance forces, kinematic slipping tangentially to moving interface, no penetration in normal direction. Problems this arise in, e.g. , FSI hydrophobic structures surfaces treated no-stick coating, biologic involving rough tissues tissue scaffolds. propose novel, efficient where sub-problem solved separately from sub-problem, there need sub-iterations at every time step achieve stability, convergence, its first-order accuracy. derive energy estimates, which prove that proposed unconditionally stable corresponding linear problem. Moreover, we convergence analysis show under time-step condition, method accurate optimally convergent space Finite Element Method-based spatial discretization. theoretical rates confirmed numerically on example explicit solution using manufactured solutions, benchmark problem propagation pressure pulse two-dimensional channel. effects rate viscosity investigated additional examples: 2D cylindrical exact Poiseuille-type found used comparison, squeezed ketchup bottle gravity enhanced flow. Navier-slip increases outflow mass 21% angled 45 degrees pointing downward, direction gravity.