Stokes Flow in an Elastic Tube { a Large-displacement Fluid-structure Interaction Problem in Print In: International Journal for Numerical Methods in Fluids

Viscous ow in elastic (collapsible) tubes is a large-displacement uid-structure interaction problem frequently encountered in biomechanics. This paper presents a robust and rapidly converging procedure for the solution of the steady three-dimensional Stokes equations, coupled to the geometrically non-linear shell equations which describe the large deformations of the tube wall. The uid and solid equations are coupled in a segregated method whose slow convergence is accelerated by an extrapolation procedure based on the scheme's asymptotic convergence behaviour. A displacement control technique is developed to handle the system's snap-through behaviour. Finally, results for the tube's post-buckling deformation and for the ow in the strongly collapsed tube are shown.