Heil, M. (1998) Stokes Flow in an Elastic Tube -- A
Large-Displacement Fluid-Structure Interaction Problem.
The International Journal for Numerical Methods in Fluids 28, 243-265.
Viscous flow in elastic (collapsible) tubes
is a large-displacement fluid-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 fluid 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 flow in the strongly collapsed tube are shown.
Page last modified: August 24, 1998
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