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Fluid-Structure Interaction Using Nonconforming Finite Element Methods

  • Edward Swim
  • Padmanabhan Seshaiyer
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)

Summary

Direct numerical solution of the highly nonlinear equations governing even the most simplified models of fluid-structure interaction requires that both the flow field and the domain shape be determined as part of the solution since neither is known a priori. To accomplish this, previous algorithms have decoupled the solid and fluid mechanics, solving for each separately and converging iteratively to a solution which satisfies both. In this paper, we describe a nonconforming finite element method which solves the problem of interaction between a viscous incompressible fluid and a structure whose deformation defines the interface between the two simultaneously. A general methodology is described for the model 2D problem and the algorithm is validated computationally for a one-dimensional example.

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References

  1. F. B. Belgacem, L. Chilton, and P. Seshaiyer. The hp mortar finite element method for the mixed elasticity and stokes problems. Comp. Math. App., 46:35–55, 2003.CrossRefGoogle Scholar
  2. F. B. Belgacem, P. Seshaiyer, and M. Suri. Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems. RAIRO Math. Mod. Numer. Anal., 34:591–608, 2000.CrossRefGoogle Scholar
  3. L. Chilton and P. Seshaiyer. The hp mortar domain decomposition method for problems in fluid mechanics. Int. Jour. Numer. Meth. Fluids, 40:1561–1570, 2002.MathSciNetCrossRefGoogle Scholar
  4. C. Grandmont, V. Guimet, and Y. Maday. Numerical analysis of some decoupling techniques for the approximation of the unsteady fluid structure interaction. Math. Mod. Meth. App. Sci., 11:1349–1377, 2001.MathSciNetCrossRefGoogle Scholar
  5. P. Seshaiyer. Stability and convergence of nonconforming hp finite-element methods. Comp. Math. App., 46:165–182, 2003.zbMATHMathSciNetCrossRefGoogle Scholar
  6. P. Seshaiyer and M. Suri. hp submeshing via non-conforming finite element methods. Comp. Meth. Appl. Mech. Engrg., 189:1011–1030, 2000a.MathSciNetCrossRefGoogle Scholar
  7. P. Seshaiyer and M. Suri. Uniform hp convergence results for the mortar finite element method. Math. Comp., 69:521–546, 2000b.MathSciNetCrossRefGoogle Scholar
  8. B. Szabo and I. Babuska. Finite element analysis. Wiley. New York, 1991.Google Scholar
  9. J. Wan, B. Steele, S. Spicer, S. Strohband, G. Feijoo, T. Hughes, and C. Taylor. A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease. Comp. Meth. Biomech. Biomed. Engrg., 2003. Submitted.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Edward Swim
    • 1
  • Padmanabhan Seshaiyer
    • 1
  1. 1.Mathematics and StatisticsTexas Tech University

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