Abstract
SUMMARY 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. 1997 by John Wiley & Sons, Ltd.
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