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Fluid–structure interaction analysis of the two-dimensional flag-in-wind problem by an interface-tracking ALE finite element method. (English) Zbl 1181.76099

Summary: J. Zhang et al. [Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835–839 (2000)] recently found that a flexible filament in a flowing soap film can exhibit three stable dynamical states; stretched-straight, flapping, and bistable states. When this experimental model is regarded as an one-dimensional flag in a two-dimensional fluid flow, their findings contradict the common idea that flags always flap in a wind. In this paper, the filament-in-soap film problem is simulated by a fluid–structure interaction finite element method as a two-dimensional version of a flag-in-wind problem, where Navier–Stokes equations based on the arbitrary Lagrangian–Eulerian (ALE) method are strongly coupled with the Lagrangian equilibrium equations of the structure. In our simulations, the three states are successfully reproduced, and the effects of some representative parameters on the amplitude and frequency of oscillations are investigated to reveal the underlying mechanism of flag flapping.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
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[1] Zhang, J.; Childress, S.; Libchaber, A.; Shelley, M., Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408, 835-839, (2000)
[2] Huber, G., Swimming in flatsea, Nature, 408, 777-778, (2000)
[3] Zhu, L.; Peskin, C.S., Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, Comput phys, 179, 452-468, (2002) · Zbl 1130.76406
[4] Zhu, L.; Peskin, C.S., Interaction of two flapping filaments in a flowing soap film, Phys fluids, 15, 7, 1954-1960, (2003) · Zbl 1186.76611
[5] Peskin, C.S., The immersed boundary method, Acta numer, 11, 479-517, (2002) · Zbl 1123.74309
[6] Zhang, Q.; Hisada, T., Analysis of fluid – structure interaction problems with structural buckling and large domain changes by ALE finite element method, Comput methods appl mech engrg, 190, 6341-6357, (2001) · Zbl 1015.74064
[7] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/petrov – galerkin formulation for convection dominated flows with particular emphasis on the incompressible navier – stokes equations, Comput methods appl mech engrg, 32, 199-259, (1982) · Zbl 0497.76041
[8] Tezduyar, T.E., Stabilized finite element formulations for incompressible flow computations, Adv appl mech, 28, 1-44, (1992) · Zbl 0747.76069
[9] Tezduyar, T.E.; Mittal, S.; Ray, S.E.; Shih, R., Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity – pressure elements, Comput methods appl mech engrg, 95, 221-242, (1992) · Zbl 0756.76048
[10] Tezduyar, T.E., Finite element methods for fluid dynamics with moving boundaries and interfaces, () · Zbl 0848.76036
[11] Dvorkin, E.N.; Bathe, K.J., A continuum mechanics based four-node shell element for general nonlinear analysis, Engrg comput, 1, 77-88, (1984)
[12] Noguchi, H.; Hisada, T., Sensitivity analysis in post-buckling problems of shell structures, Comput struct, 47, 4, 699-710, (1993) · Zbl 0782.73070
[13] Tezduyar, T.E.; Behr, M.; Mittal, S.; Johnson, A.A., Computation of unsteady incompressible flows with the stabilized finite element methods-space-time formulations, iterative strategies and massively parallel implementations, (), 7-24
[14] Johnson, A.A.; Tezduyar, T.E., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Comput methods appl mech engrg, 119, 73-94, (1994) · Zbl 0848.76036
[15] Stein, K.; Tezduyar, T.; Benney, R., Mesh moving techniques for fluid – structure interactions with large displacements, J appl mech, 70, 58-63, (2003) · Zbl 1110.74689
[16] Tezduyar TE, Sathe S, Keedy R, Stein K. Space – time finite element techniques for computation of fluid – structure interactions. Comput Methods Appl Mech Engrg, in press. · Zbl 1118.74052
[17] Martin, B.; Wu, X.-I., Shear flow in a two-dimensional Couette cell: a technique for measuring the viscosity of free-standing liquid films, Rev sci instrum, 66, 12, 5603-5608, (1995)
[18] Cortez, R.; Peskin, C.S.; Stockie, J.M.; Varela, D., Parametric resonance in immersed elastic boundaries, SIAM J appl math, 65, 494-520, (2004) · Zbl 1074.74024
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