The enriched space-time finite element method (EST) for simultaneous solution of fluid-structure interaction

International Journal for Numerical Methods in Engineering

Volumn 75, Issue 3, 2008, Pages 305-334

  Zilian, A ^a   Legay, A ^b  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b Bioinformatique et Chimie Moléculaire   (France)

Author keywords

Enriched space time finite elements; EST method; Fluid structure interaction; Level set method

Indexed keywords

COMPUTATIONAL METHODS; EQUATIONS OF MOTION; FLEXIBLE STRUCTURES; FLOW INTERACTIONS; FLOW OF FLUIDS; FLUID DYNAMICS; FLUID MECHANICS; FLUID STRUCTURE INTERACTION; FLUIDS; INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; MATERIALS SCIENCE; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; OPTICAL TOMOGRAPHY; SET THEORY; SOLUTIONS; STRUCTURAL DYNAMICS;

ALGEBRAIC SYSTEMS; COUPLED SYSTEMS; COUPLING CONDITIONS; CURRENT CONFIGURATION; DISCONTINUOUS SOLUTIONS; DISCRETIZATION; DISTRIBUTED LAGRANGE MULTIPLIERS; ENRICHED SPACE-TIME FINITE ELEMENTS; EST METHOD; EXTENDED FINITE ELEMENT METHOD; FINITE-ELEMENT DISCRETIZATION; FLUID FLOWING; FLUID PRESSURES; FLUID-STRUCTURE SYSTEMS; INCOMPRESSIBLE NAVIER-STOKES EQUATIONS; INTERFACIAL CONSTRAINTS; LEVEL SET FUNCTIONS; LEVEL SET METHOD; LINEAR ELASTIC MATERIALS; MULTI-FIELD PROBLEM; NON-LINEAR; NUMERICAL APPROACHES; NUMERICAL EXAMPLES; NUMERICAL INVESTIGATIONS; SIMULTANEOUS SOLUTION; SPACE-TIME FINITE ELEMENT METHODS; STRUCTURAL MOTIONS; TEST CASES; THIN STRUCTURES; WEAK FORM;

FINITE ELEMENT METHOD;

EID: 48549097062     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2258     Document Type: Article

References (39)

1. Nomura T. ALE finite element computations of fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 1994; 146:91-126.
2. Bathe K-J, Zhang H, Ji S. Finite element analysis of fluid flows fully coupled with structural interaction. Computers and Structures 1999; 72(1-3):1-16.
3. Wall WA, Mok DP, Ranun E. Partitioned analysis approach for the transient coupled response of viscous fluids and flexible structures. In Proceedings of the European Conference on Computational Mechanics, ECCM'99, Munich, Wunderhch W (ed.), 1999.
4. Kuhl E, Hulshoff S, de Borst R. An arbitrary Lagrangian-Eulerian finite-element approach for fluid-structure interaction phenomena. International Journal for Numerical Methods in Engineering 2003; 57:117-142.
5. Le Tallec P, Mouro J. Fluid-structure interaction with large structural displacements. Computer Methods in Applied Mechanics and Engineering 2001; 190(24-25):3039-3067.
6. Peskin CS, McQueen DM. A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. Journal of Computational Physics 1989; 81(2):372-405.
7. Bertrand F, Tanguy PA, Thibault F. A three-dimensional fictitious domain method for incompressible fluid flow problems. International Journal for Numerical Methods in Fluids 1997; 25(6):719-736.
8. Glowinski R, Pan TW, Hesla TI, Joseph DD. A distributed Lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow 1999; 25(5):755-794.
9. Zhang L, Gerstenberger A, Wang X, Liu WK. Immersed finite element method. Computer Methods in Applied Mechanics and Engineering 2004; 193(21-22):2051-2067.
10. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4):993-1013.
11. Sethian JA. Level Set Methods and Fast Marching Methods. Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press: Cambridge, 1999.
12. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):289-314.
13. Chessa J, Belytschko T. An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. International Journal for Numerical Methods in Engineering 2003; 58(13):2041-2064.
14. Sukumar N, Chopp D, Moës N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 190(46-47):6183-6200.
15. Moës N, Dolbow JE, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
16. Legay A, Chessa J, Belytschko T. An Eulerian-Lagrangian method for fluid-structure interaction based on level sets. Computer Methods in Applied Mechanics and Engineering 2006; 195(17-18):2070-2087.
17. Legay A, Tralli A. An Euler-Lagrange enriched finite element approach for fluid-structure interaction. European Journal of Computational Mechanics 2007; 16(2):145-160.
18. Kölke A, Walborn E, Hübner B, Dinkler D. Numerical modeling of fluid-structure interaction with free surface flows. Proceedings in Applied Mathematics and Mechanics 2003; 3(1):412-413 (Available from: http://www3.interscience.wiley.com/cgi-bin/fulltext /106571654/PDFSTART).
19. Chessa J, Belytschko T. Arbitrary discontinuities in space-time finite elements by level sets and X-FEM. International Journal for Numerical Methods in Engineering 2004; 61(15):2595-2614.
20. Chessa J, Belytschko T. A local space-time discontinuous finite element method. Computer Methods in Applied Mechanics and Engineering 2006; 195(13-16):1325-1343.
21. Tezduyar TE, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Computer Methods in Applied Mechanics and Engineering 1992; 94(3):339-351.
22. Hughes TJP, Hulbert GM. Space-time finite element methods for elastodynamics: formulations and error estimates. Computer Methods in Applied Mechanics and Engineering 1988; 66(3):339-363.
23. Tezduyar TE, Behr M, Mittal S. A new strategy for finite element computations involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Computer Methods in Applied Mechanics and Engineering 1992; 94(3):353-371.
24. Hübner B, Walborn E, Dinkler D. Numerical investigations to bridge aeroelasticity. In Proceedings of the Fifth World Congress on Computational Mechanics, Vienna, Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds), 2002. http://wccm.tuwien.ac.at/publications/ Papers/fp81407.pdf.
25. Hübner B, Walborn E, Dinkler D. A monolithic approach to fluid-structure interaction using space-time finite elements. Computer Methods in Applied Mechanics and Engineering 2004; 193(23-26):2087-2104.
26. Kölke A, Dinkier D. Extended space-time finite elements for two-fluid flows in fluid-structure interaction. In Proceedings of Sixth World Congress on Computational Mechanics, Beijing, Yao ZH, Yuan MW, Zhong WX (eds), 2004.
27. Walborn E, Kölke A, Hübner B, Dinkler D. Fluid-structure coupling within a monolithic model involving free surface flows. Computers and Structures 2005; 83(25-26):2100-2111.
28. Kölke A, Dinkler D. Extended space-time finite elements for boundary-coupled multi-field problems on fixed grids. In International Conference on Computational Methods for Coupled Problems in Science and Engineering, Santorini, Papadrakakis M, Oňate E, Schrefler B (eds), 2005.
29. Legay A, Kölke A. An enriched space-time finite element method for fluid-structure interaction - Part 1: prescribed structural displacement. Proceedings of the Third European Conference on Computational Mechanics, Lisbon, 2006.
30. Kölke A, Legay A. An enriched space-time finite element method for fluid-structure interaction - Part II: thin flexible structures. Proceedings of the Third European Conference on Computational Mechanics, Lisbon, 2006.
31. Felippa C. The TL Timoshenko Plane Beam Element, Chapter 9, Nonlinear Finite Element Methods (ASEN 5107), 2007 (Available from: http://www.colorado.edu/engineering/CAS/courses.d/NFEM.d).
32. Argyris JH, Scharpf D. Finite elements in space and time. Journal of the Royal Aeronautical Society 1969; 73:1041-1044.
33. Masud A, Hughes TJR. A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems. Computer Methods in Applied Mechanics and Engineering 1997; 146(1-2):91-126.
34. Kölke A. Modellierung und Diskretisierung bewegter Diskontinuitäten in randgekoppelten Mehrfeldsystemen. Ph.D. Thesis, Technische Universität Braunschweig, 2005 (Available from: http://www.digibib.tu-bs.de/?docid=00001723).
35. Chessa J, Wang HW, Belytschko T. On the construction of blending elements for local partition of unity enriched finite elements. International Journal for Numerical Methods in Engineering 2003; 57(7):1015-1038.
36. Ji H, Dolbow J. On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method. International Journal for Numerical Methods in Engineering 2004; 61:2508-2535.
37. Moës N, Béchet E, Tourbier M. Imposing Dirichlet boundary conditions in the extended finite element method. International Journal for Numerical Methods in Engineering 2006; 67:1641-1669.
38. Hansbo P, Lovadina C, Perugia I, Sangalli G. A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes. Numerische Mathematik 2005; 100:91-115.
39. Gielis J. A generic geometric transformation that unifies a wide range of natural and abstract shapes. American Journal of Botany 2003; 90(3):333-338.