Abstract
A simplified formulation of the fluid-structure interaction problem is presented in order to analyze the coupling conditions and the effect of a moving fluid domain on the numerical solution. The resulting one-dimensional model equations are discretized by the finite element method in space and then solved by implicit timestepping schemes, with the coupling conditions explicitly enforced by means of corresponding constraint equations in a differential-algebraic formulation. First numerical results indicate an influence of the moving fluid mesh on the stability properties of commonly used time integrators.
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References
Boffi, D., Gastaldi, L.: Stability and geometric conservation laws for ale formulations. Comput. Methods Appl. Mech. Eng. 193, 4717–4739 (2004)
Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)
Doerfel, M.R., Simeon, B.: Fluid-structure-interaction: acceleration of strong coupling by preconditioning of the fixed-point iteration. In: Proceedings of the ENUMATH 2011 Conference (2011)
Donea, J., Huerta, A.: Finite Element Methods for Flow Problems. Wiley, New York (2003)
Farhat, C., Lesoinne, M., Maman, N.: Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometry conservation and distributed solution. Int. J. Numer. Methods Fluids 21, 807–835 (1995)
Formaggia, L., Nobile, F.: A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. East West J. Numer. Math. 7, 105–132 (1999)
Gastaldi, L.: A priori error estimates for the arbitrary Lagrangian Eulerian formulation with finite elements. East West J. Numer. Math. 9, 123–156 (2001)
Hairer, E., Norsett, S., Wanner, G.: Solving Ordinary Differential Equations I. Springer, New York (1987)
Nobile, F.: Numerical approximation of fluid-structure interaction problems with applications to haemodynamics. Ph.D. thesis, Department of Mathematics, école Polytechnique Fédèrale de Lausanne, Switzerland (2001)
Wall, W.A.: Fluid-Struktur-Interaktion mit stabilisierten Finiten-Elementen. Ph.D. thesis, Institut für Baumechanik, Universität Stuttgart (1999)
Wick, T.: Fluid-structure interactions using different mesh motion techniques. Comput. Struct. 89, 1456–1467 (2011)
Acknowledgements
Supported within the BMBF project: SNiMoRed, Multidisziplinäre Simulation, nichtlineare Modellreduktion und proaktive Regelung in der Fahrzeugdynamik.
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Niemeyer, J., Simeon, B. (2014). Modelling of a Simplified Fluid-Structure Interaction Formulation. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_22
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DOI: https://doi.org/10.1007/978-3-319-05365-3_22
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