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Finite element computations for unsteady fluid and elastic membrane interaction problems

✍ Scribed by S.-J. Liang; G. P. Neitzel; C. K. Aidun

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 391 KB
Volume: 24
Category: Article
ISSN: 0271-2091
DOI: 10.1002/(sici)1097-0363(19970615)24:11<1091::aid-fld520>3.0.co;2-q

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✦ Synopsis

The interaction between the hydrodynamic forces of a flow field and the elastic forces of adjacent deformable boundaries is described by elastohydrodynamics, a coupled fluid-elastic membrane problem. Direct numerical solution of the unsteady, highly non-linear equations requires that the dynamic evolution of both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. This paper describes a numerical algorithm based on the deformable spatial domain space-time (DSD=ST) finite element method for the unsteady motion of an incompressible, viscous fluid with elastic membrane interaction. The unsteady Navier-Stoke and elastic membrane equations are solved separately using an iterative procedure by the GMRES technique with an incomplete lower-upper (ILU) decomposition at every time instant. One-dimensional, twodimensional and deformable domain model problems are used to demonstrate the capabilities and accuracy of the present algorithm. Both steady state and transient problems are studied.

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