FINITE-ELEMENT COMPUTATIONS FOR UNSTEADY FLUID AND ELASTIC MEMBRANE INTERACTION PROBLEMS

The interaction between the hydrodynamic forces of a flow field and th e elastic forces of adjacent deformable boundaries is described by ela stohydrodynamics, a coupled fluid-elastic membrane problem. Direct num erical 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 prior i. This paper describes a numerical algorithm based on the deformable spatial domain space-time (DSD/ST) finite element method for the unste ady motion of an incompressible, viscous fluid with elastic membrane i nteraction. The unsteady Navier-Stoke and elastic membrane equations a re solved separately using an iterative procedure by the GMRES techniq ue with an incomplete lower-upper (ILU) decomposition at every time in stant. One-dimensional, two-dimensional and deformable domain model pr oblems are used to demonstrate the capabilities and accuracy of the pr esent algorithm. Both steady state and transient problems are studied. (C) 1997 by John Wiley & Sons, Ltd.