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THE NUMERICAL SIMULATION OF LARGE-SCALE FLUID-STRUCTURE INTERACTION PROBLEMS IN A FULLY COUPLED FORM

Eken, A.; Sahin, M.;

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A fully coupled numerical algorithm has been developed for the numerical simulation of large-scale fluid structure interaction problems. The incompressible Navier-Stokes equations are discretized using an Arbitrary Lagrangian-Eulerian (ALE) formulation based on the side-centered unstructured finite volume method. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure-velocity coupling. A special attention is given to satisfy the discrete continuity equation within each element at discrete level as well as the Geometric Conservation Law (GCL). The nonlinear elasticity equations are discretized within the structure domain using the Galerkin finite element method. The resulting algebraic linear equations are solved in a fully coupled form. The implementation of the fully coupled preconditioned iterative solvers is based on the PETSc library for improving th! e efficiency of the parallel code. The present numerical algorithm is initially validated for a Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder and a three-dimensional elastic solid confined in a rectangular channel. ical Galerkin finite element is used to discretize the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized− method while the first-order backward difference is used in the fluid domain. The implementation of the preconditioned coupled iterative solvers is based on the PETSc library for improving the efficiency of the parallel code. The present numerical algorithm is validated for a steady and unsteady Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder and a three-dimensional elastic solid confined in a rectangular channel.

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Palavras-chave: Fluid-Structure Interaction, Unstructured Finite Volume Method, Finite Element Method, Large Displacement, Large-Scale Computation, Monolitic Method.,

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DOI: 10.5151/meceng-wccm2012-18908

Referências bibliográficas
  • [1] W. K. Anderson and D. L. Bonhaus, An implicit upwind algorithm for computing turbulent flows on unstructured grids. Comp. Andamp; Fluids 23, (1994), 1–2
  • [2] S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, B. F. Smith and H. Zhang, PETSc Users Manual. ANL-95/11, Mathematic and Computer Science Division, Argonne National Laboratory, (2004). http://wwwunix. mcs.anl.gov/petsc/petsc-2/
  • [3] A. T. Barker and X.-C. Cai, Scalable parallel methods for monolithic coupling in fluidstructure interaction with application to blood flow modeling. J. Comput.Phys. 229, (2010), 642–659.
  • [4] T. J. Barth, A 3-D upwind Euler solver for unstructured meshes. AIAA Paper 91-1548- CP, (1991).
  • [5] J. T. Batina. Unsteady Euler airfoil solutions using unstructured dynamic meshes. AIAA J. 28, (1990), 1381-1388.
  • [6] M. Behr, T. E. Tezduyar, Finite element solution strategies for large-scale flow simulations. Comput. Methods Appl. Mech. Engrg. 112, (1994), 3–24.
  • [7] T. D. Blacker, S. Benzley, S. Jankovich, R. Kerr, J. Kraftcheck, R. Kerr, P. Knupp, R. Leland, D. Melander, R. Meyers, S. Mitchell, J. Shepard, T. Tautges and D. White, CUBIT Mesh Generation Enviroment Users Manual Volume 1. Sandia National Laboratories: Albuquerque, NM (1999).
  • [8] F. J. Blom, A monolithical fluid-structure interaction algorithm applied to the piston problem. Methods Appl. Mech. Engrg. 167, (1998), 369–391.
  • [9] J. Chung and G. M. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- method. J. Appl. Math. 60, (1993), 371–375.
  • [10] A. J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comp. 22, (1968), 745–762.
  • [11] E. Cuthill and J. McKee, Reducing the bandwidth of sparce symmetric matrices. 24th. ACM National Conference, (1969), 157–172.
  • [12] M. Dai, D.P. Schmidt, Adaptive tetrahedral meshing in free-surface flow, J. Comput. Phy. 208 (2005), 228–252.
  • [13] J. Donea, S. Jiuliani, and J. P. Halleux. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comp. Meth. Appl. Mech. Eng. 33, (1982), 689–723.
  • [14] C. Farhat. CFD-based nonlinear computational aeroelasticity. Encyclopedia of computational mechanics 3, (2004), 459–480, E. Stein, R. De Borst and T. Hughes (Eds), John Wiley Andamp; Sons.
  • [15] M. W. Gee, U. Küttler and W. A. Wall, Truly monolithic algebraic multigrid for fluidstructure interaction. Int. J. Numer. Meth. Engng 85, (2011), 987–1016.
  • [16] M. Heil, A. L. Hazel and J. Boyle, Solvers for large-displacement fluidstructure interaction problems: segregated versus monolithic approaches. Comput. Mech. 43, (2008), 91–101.
  • [17] R. Falgout, A. Baker, E. Chow, V. E. Henson, E. Hill, J. Jones, T. Kolev, B. Lee, J. Painter, C. Tong, P. Vassilevski and U. M. Yang, Users manual, HYPRE High Performance Preconditioners. UCRL-MA-137155 DR, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, (2002). http://www.llnl.gov/CASC/hypre/
  • [18] T. Gerhold and J. Neumann, The parallel mesh deformation of the DLR TAU-code. New Results in Numerical and Experimental Fluid Mechanics VI 96, (2007), 162–169.
  • [19] W. Hackbusch, Multigrid methods and applications. Springer-Verlag, Heidelberg, (1985).
  • [20] F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. J. Comput. Phys. 8, (1965), 2182–2189.
  • [21] C. W. Hirt, A. A. Amsden and J. L. Cook, An arbitrary LagrangianEulerian computing method for all flow speeds. J. Comput. Phys. 14, (1974), 227–253.
  • [22] J. Hron, S. Turek, Proposal for numerical benchmarking of fluidstructure interaction between an elastic object and laminar incompressible flow. FluidStructure Interaction: Modeling, Simulation, Optimization, Lecture Notes in Computational Science and Engineering 53, (2006), Hans-Joachim Bungartz, Michael Schafer (Eds.), Springer, 146–170.
  • [23] T. J. R. Hughes, W. K. Liu, and T. Zimmerman, Lagrangian-Eulerian finite element formulation for incompressible viscous flow. Comp. Meth. Appl. Mech. Eng. 29,(1981), 329-349.
  • [24] Y. H. Hwang, Calculations of incompressible flow on a staggered triangle grid, Part I: Mathematical formulation. Numer. Heat Transfer B 27, (1995), 323–1995.
  • [25] A. A. Johnson, T. E. Tezduyar, Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput. Methods Appl. Mech. Engrg. 119, (1994) 73–94.
  • [26] A. Johnson, T. Tezduyar, Advanced mesh generation and update methods for 3D flow simulations. Comput. Mech. 23, (1999) 130–143.
  • [27] G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20, (1998), 359–392.
  • [28] N. M. Newmark, A method of computation for structural dynamics. Journal of the Engineering Mechanics Division (ASCE) 85, (1959), 67–94.
  • [29] K. C. Park, C. A. Felippa, and J. A. Deruntz. Stabilization of staggered solution procedures for fluidstructure interaction analysis. Computational Methods for Fluid-Structure Interaction Problems, (1977), 94–124, T. Belytschko and T. L. Geers, (Eds.), ASME.
  • [30] T. Richter, Goal-oriented error estimation for fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg., (submitted).
  • [31] S. Rida, F. McKenty, F. L. Meng and M. Reggio, A staggered control volume scheme for unstructured triangular grids. Int. J. Numer. Meth. Fluids 25, (1997), 697–717.
  • [32] Y. Saad, A flexible inner-product preconditioned GMRES algorithm. SIAM J. Sci. Statist. Comput. 14, (1993), 461–469.
  • [33] M. Sahin, A stable unstructured finite volume method for parallel large-scale viscoelastic fluid flow calculations. Journal of non-Newtonian Fluid Mechanics 166, (2011), 779– 791.
  • [34] M. Sahin and K. Mohseni, An Arbitrary Lagrangian-Eulerian Formulation for the Numerical Simulation of Flow Patterns Generated by the Hydromedusa Aequorea Victoria. J. Comput. Phys. 228, (2009), 4588–4605.
  • [35] P. D. Thomas and C. K. Lombard, Geometric conservation law and its application to flow computations on moving grids. AIAA J. 17, (1979), 1030–1037.
  • [36] P. Wesseling, An introduction to multigrid methods. John Wiley Andamp; Sons, New York, (1992).
  • [37] E. L. Wilson, R. L. Taylor, W. P. Doherty and J. Ghaboussi, Incompatible displacement models. Numerical and Computer Methods in Structural Mechanics, S.J. Fenves et al., Eds., Academic Press, New York, (1973) 43–58.
  • [38] J. Degroote , R. Haelterman , S. Annerel , P. Bruggeman , J. Vierendeel, Performance of partitioned procedures in fluid-structure interaction. Comput Struct 88, (2010), 446–457.
  • [39] Th. Richter , Th. Wick, Finite elements for fuid-structure interaction in ALE and fully Eulerian coordinates. Comput. Methods Appl. Mech. Engrg. 199, (2010), 2633–2642.
  • [40] Th. Wick, Solving Monolithic Fluid-Structure Interaction Problems in Arbitrary Lagrangian Eulerian Coordinates with the deal.II Library. IWR Report, University of Heidelberg, Germany, (2011).
  • [41] V. Chabannes, G. Pena, C. Prudhomme, High order fluid structure interaction in 2D and 3D Application to blood flow in arteries. Preprint submitted to J. Comput. Appl. Math., (2012).
Como citar:

Eken, A.; Sahin, M.; "THE NUMERICAL SIMULATION OF LARGE-SCALE FLUID-STRUCTURE INTERACTION PROBLEMS IN A FULLY COUPLED FORM", p. 2559-2577 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18908

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