Coupled systems mechanics

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Algorithm for solving fluid-structure interaction problem on a global moving mesh

  • Sy, Soyibou (Laboratoire de Mathematiques, Informatique et Applications, Universite de Haute Alsace) ;
  • Murea, Cornel Marius (Laboratoire de Mathematiques, Informatique et Applications, Universite de Haute Alsace)
  • Received : 2011.10.14
  • Accepted : 2012.03.13
  • Published : 2012.03.25
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Abstract

We present a monolithic semi-implicit algorithm for solving fluid-structure interaction problem at small structural displacements. The algorithm uses one global mesh for the fluid-structure domain obtained by gluing the fluid and structure meshes which are matching on the interface. The continuity of velocity at the interface is automatically satisfied and the continuity of stress does not appear explicitly in the global weak form due to the action and reaction principle. At each time step, we have to solve a monolithic system of unknowns velocity and pressure defined on the global fluid-structure domain. Numerical results are presented.

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References

  1. Badia, S., Quaini, A. and Quarteroni, A. (2008a), "Splitting methods based on algebraic factorization for fluidstructure interaction", SIAM J. Sci. Comput., 30(4), 1778-1805. https://doi.org/10.1137/070680497
  2. Badia, S., Quaini, A. and Quarteroni, A. (2008b), "Modular vs. non-modular preconditioners for fluidstructure systems with large added-mass effect", Comput. Method. Appl. M., 197(49-50), 4216-4232. https://doi.org/10.1016/j.cma.2008.04.018
  3. Dunne, T. (2006),"An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaptation", Int. J. Num. Meth. Fl., 51(9-10), 1017-1039. https://doi.org/10.1002/fld.1205
  4. Fernandez, M.A., Gerbeau, J.F. and Grandmont, C. (2007), "A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid", Int. J. Numer. Meth. Eng., 69(4), 794-821. https://doi.org/10.1002/nme.1792
  5. Hecht, F., Pironneau, O., Le Hyaric, A. and Ohtsuka, K. (2005), FreeFem++: http://www.freefem++.org/ff++.
  6. Hron, J. and Turek, S. (2006), A monolithic FEM/multigrid solver for an ALE formulation of fluidstructure interaction with application in biomechanics, In Fluid-Structure Interaction, Lect. Notes. Comput. Sci. Eng. 53, 146-170, Springer, Berlin.
  7. Heil, M., Hazed, A.L. and Boyle, J. (2008),"Solvers for large-displacement fluid-structure interaction problems: segregated versus monolithic approaches", Comput. Mech., 193(1-2), 91-101.
  8. Hubner, B., Walhorn, E. and Dinkler, D. (2004), "A monolithic approach to fluid-structure interaction using space-time finite elements", Comput. Meth. Appl., 193(23-26), 2087-2104. https://doi.org/10.1016/j.cma.2004.01.024
  9. Murea, C.M. (2008), "A semi-implicit algorithm based on the Augmented Lagrangian Method for fluid-structure interaction", Num. Math. Adv. App, Proceedings of the ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, Springer, 555-562.
  10. Murea, C.M. and Sy, S. (2009), "A fast method for solving fluid-structure interaction problem numerically", Int. J. Numer. Meth. Fl, 60(10), 1149-1172. https://doi.org/10.1002/fld.1931
  11. Sy, S. and Murea, C.M. (2008), "A stable time advancing scheme for solving fluid-structure interaction problem at small structural displacements", Comput. Meth. Appl. Mech., 198(2), 210-222. https://doi.org/10.1016/j.cma.2008.07.010
  12. Tezduyar, T., Sathe, S., Keedy, R. and Stein, K. (2006), "Space-time finite element techniques for computation of fluidstructure interactions", Comput. Meth. Appl. Mech., 195(17-18), 2002-2027. https://doi.org/10.1016/j.cma.2004.09.014
  13. Quaini, A. and Quarteroni, A. (2007), "A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method", Math. Mod. Meth. Appl. S., 17(6), 957-983. https://doi.org/10.1142/S0218202507002170
  14. Quarteroni, A. and Formaggia, L. (2004), Mathematical modelling and numerical simulation of the cardiovascular system, (Ed. P.G. Ciarlet), Handbook of numerical analysis, vol. XII, North-Holland, Amsterdam, 3-127.

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  2. Three-Dimensional Simulation of Fluid-Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm vol.4, pp.2, 2019, https://doi.org/10.3390/fluids4020094