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Fluid-Structure Interaction by the Spectral Element Method

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Viscous fluid-structure interaction is treated with an arbitrary Lagrangian- Eulerian formulation. The spatial discretization is performed by the spectral element method for the fluid part where the Navier-Stokes equations are integrated and in the solid part where transient linear elasticity is described by the Navier equations. Time marching algorithms are second-order accurate in time in both the fluid and the solid. The algorithm is applied to the flow in a plane channel partially obstructed by a solid component able to move under the action of the fluid flow.

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References

  1. Formaggia L., Gerbeau J.-F., Nobile F., Quarteroni A. (2001). On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput. Meth. Appl. Mech. Engrg. 191, 561–582

    Article  MathSciNet  Google Scholar 

  2. Le Tallec P., Mouro J. (2001). Fluid-structure interaction with large structural displacement. Comput. Meth. Appl. Mech. Engrg. 190, 3039–3067

    Article  Google Scholar 

  3. Ramaswamy B., Kawahara M. (1987). Arbitrary Lagrangian-Eulerian finite element method for unsteady, convective, incompressible viscous free surface fluid flow. In: Gallagher R.H., Glowinsky R., Gresho P.M., Oden J.T., Zienkiewicz O.C. (eds). Finite Elements in Fluids-Volume 7. John Wiley and Sons Ltd., New York, pp. 65–87

    Google Scholar 

  4. Blom F. (1998). Investigation on computational fluid-structure interaction, Ph.D. n 1865, EPFL, Lausanne

    Google Scholar 

  5. Glowinski R., Pan T.-W., Periaux J. (1994). A ficticious domain method for Dirichlet problem and applications. Comput. Meth. Appl. Mech. Engrg. 111, 283–303

    Article  MathSciNet  Google Scholar 

  6. De Hart J., Peters G.W.M., Schreurs P.J.G., Baaijens F.P.T. (2000). A two-dimensional fluid-structure interaction model of the aortic valve. J. Biomech. 33, 1079–1088

    Article  PubMed  Google Scholar 

  7. Causin P., Gerbeau J.F., Nobile F., (2005). Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput. Methods Appl. Mech. Engrg. 193, 4073–4095

    MathSciNet  Google Scholar 

  8. Ho L.-W., Patera A.T. (1990). A Legendre Element Method for Simulation of Incompressible Unsteady Viscous Free-surface Flows. Comput. Methods Appl. Mech. Engrg. 80, 355–366

    Article  MathSciNet  Google Scholar 

  9. Deville M.O., Fischer P.F., Mund E.H. (2002). High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge

    Google Scholar 

  10. Widlund O.B., Pavarino L.F. (1999). Iterative substructuring methods for spectral element discretizations of elliptic systems.II: mixed methods for linear elasticity and Stokes flow. SIAM J. Numer. Anal. 37(2): 375–402

    Article  MathSciNet  Google Scholar 

  11. Casadei F., Gabellini E., Fotia G., Maggio F., Quarteroni A. (1993). A mortar spectral/finite element method for complex 2D and 3D elastodynamic problems. Comput. Meth. Appl. Mech. Engrg. 104, 49–76

    Article  Google Scholar 

  12. Donea J., Guiliani S., Halleux J.P. (1982). An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput. Meth. Appl. Mech. Engrg. 33, 689–723

    Article  Google Scholar 

  13. Formaggia L., Nobile F. (2004). Stability analysis of second-order time accurate schemes for ALE-FEM. Comput. Methods Appl. Mech. Engrg. 193, 4097–4116

    Article  MathSciNet  Google Scholar 

  14. Boffi D., Gastaldi L. (2004). Stability and geometric conservation laws for ALE formulations. Comput. Methods Appl. Mech. Engrg. 193, 4717–4739

    Article  MathSciNet  Google Scholar 

  15. Maday Y., Patera A.T. (1989). Spectral element methods for the Navier-Stokes equations. In: Noor A.K., Oden J.T. (eds). State-of-the-Art Surveys in Computational Mechanics. ASME, New York, pp. 71–143

    Google Scholar 

  16. Couzy W., Deville M.O. (1994). Spectral-element preconditoners for the Uzawa pressure operator applied to incompressible flows. J. Sci. Comput. 9, 107–112

    Google Scholar 

  17. Perot J.B. (1993). An analysis of the fractional step method. J. Comp. Phys. 108, 51–58

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. Curnier A. (1993). Méthodes numériques en mécanique des solides. Presses polytechniques et universitaires romandes, Lausanne

    Google Scholar 

  19. Dubois-Pèlerin Y., Van Kemenade V., Deville M.O. (1999). An Object-Oriented Toolbox for Spectral Element Analysis. J. Sci. Comput. 14, 1–29

    Article  MathSciNet  Google Scholar 

  20. Farhat C., Lesoinne M. (2000). Two efficient staggered algorithms for serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Meth. Appl. Mech. Engrg. 182, 499–515

    Article  Google Scholar 

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  1. Ecole Polytechnique Fédérale de Lausanne, Laboratory of Computational Engineering, CH-1015, Lausanne, Switzerland

    N. Bodard & M. O. Deville

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  1. N. Bodard
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  2. M. O. Deville
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Bodard, N., Deville, M.O. Fluid-Structure Interaction by the Spectral Element Method. J Sci Comput 27, 123–136 (2006). https://doi.org/10.1007/s10915-005-9031-2

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  • DOI: https://doi.org/10.1007/s10915-005-9031-2

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