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Stokes flow in an elastic tube—a large‐displacement fluid‐structure interaction problem
Author(s) -
Heil Matthias
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19980815)28:2<243::aid-fld711>3.0.co;2-u
Subject(s) - stokes flow , displacement (psychology) , mechanics , fluid–structure interaction , extrapolation , flow (mathematics) , convergence (economics) , tube (container) , fluid dynamics , deformation (meteorology) , classical mechanics , mathematical analysis , mathematics , physics , finite element method , engineering , mechanical engineering , thermodynamics , psychology , psychotherapist , meteorology , economics , economic growth
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. © 1998 John Wiley & Sons, Ltd.