Fluid-structure interaction by the discontinuous-Galerkin method for large deformations

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 1, 2009, Pages 30-49

  Wang, Hongwu ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

Discontinuous Galerkin; Eulerian; Fluid structure interaction; Lagrangian; Large deformation

Indexed keywords

DEFORMATION; FLUID DYNAMICS; FLUIDS; GALERKIN METHODS; LAGRANGE MULTIPLIERS;

DISCONTINUOUS GALERKIN; ELEMENT METHODS; EULERIAN; EULERIAN DESCRIPTIONS; FLUID-STRUCTURE INTERACTION PROBLEMS; FLUID-STRUCTURE INTERFACES; LAGRANGIAN; LAGRANGIAN DESCRIPTIONS; LARGE DEFORMATION;

FLUID STRUCTURE INTERACTION;

EID: 60949086364     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2396     Document Type: Article

References (39)

1. Belytschko T, Kennedy JM. Computer models for subassembly simulation. Nuclear Engineering and Design 1978; 49:17-38.
2. Belytschko T. Fluid-structure interaction. Computers and Structures 1980; 12:459-469.
3. Hughes TJR, Liu WK, Zimmermann TK. Lagrangian-Eulerian finite element formulation for viscous flows. Computer Methods in Applied Mechanics and Engineering 1981; 29:329-349.
4. Idelsohn SR, Oñate E, Calvo N, Del Pin F. The meshless finite element method. International Journal for Numerical Methods in Engineering 2003; 58:893-912.
5. Arnold DN. An interior penalty finite element method with discontinuous elements. SIAM Journal on Numerical Analysis 1982; 19(4):742-760.
6. Peskin CS. Numerical analysis of blood flow in the heart. Journal of Computational Physics 1977; 25:220-252.
7. Peskin CS. The immersed boundary method. Acta Numerica 2002; 11:479-517.
8. Leveque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM Journal on Numerical Analysis 1994; 31:1019-1044.
9. Wang X, Liu WK. Extended immersed boundary method using FEM and RKPM. Computer Methods in Applied Mechanics and Engineering 2004; 193:1305-1321.
10. Zhang L, Gerstenberger A, Wang X, Liu WK. Immersed finite element method. Computer Methods in Applied Mechanics and Engineering 2004; 193:2051-2067.
11. Liu WK, Kim DW, Tang S. Mathematical foundations of the immersed finite element method. Computational Mechanics 2007; 39(3):211-222.
12. Wang HW, Chessa J, Liu WK, Belytschko T. The immersed/fictitious element method for fluid-structure interaction: volumetric consistency, compressibility and thin members. International Journal for Numerical Methods in Engineering 2007; 74(1):32-55.
13. Glowinski R, Pan TW, Hesla TI, Joseph DD. A distributed Lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow 1999; 24:755-794.
14. Glowinski R, Pan TW, Hesla TI, Joseph DD, Périaus J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particular flow. Journal of Computational Physics 2001; 169:363-426.
15. Patankar NA, Singh P, Joseph DD, Glowinski R, Pan TW. A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow 2000; 26: 1509-1524.
16. Baaijens FPT. A fictitious domain/mortar element method for fluid-structure interaction. International Journal for Numerical Methods in Fluids 2001; 35:743-761.
17. Hart JD, Baaijens FPT, Peters GWM, Schreurs PJG. A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. Journal of Biomechanics 2003; 36:699-712.
18. 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; 195:2070-2087.
19. 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.
20. Chessa J, Belytschko T. An extended finite element method for two-phase fluids. Journal of Applied Mechanics - Transactions of the ASME 2003; 70(1):10-17.
21. 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.
22. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
23. Gerstenberger A, Wall WA. An extended finite element method/Larange multiplier based approach for fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering 2008; 197:1699-1714.
24. Zhang L, Tezaur R, Farhat C. The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime. International Journal for Numerical Methods in Engineering 2006; 66:2086-2114.
25. Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilraümen, die keinen Randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1971; 36:9-15.
26. Arnold DN, Brezzi F, Cockburn B, Marini L. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis 2002; 39(5):1749-1779.
27. Reed WH, Hill TR. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
28. Riviere B, Wheeler MF. A discontinuous Galerkin method applied to nonlinear parabolic equations. In Discontinuous Galerkin Methods: Theory, Computation and Applications, vol. 11, Cockburn B, Karniadakis G, Shu CW (eds). Springer: Berlin, 2000; 231-244.
29. Babuǔka I, Baumann CE, Oden JT. A discontinuous hp finite element method for diffusion problems: 1-D analysis. Computers and Mathematics with Applications 1999; 37(9):103-122.
30. Karniadakis G, Sherwin SJ. Spectral/hp Element Methods for CFD. Oxford University Press: Oxford, 1999.
31. Cockburn B. Discontinuous Galerkin methods. Zeitschrift fur Angewandte Mathematik und Mechanik 2003; 83(11):731-754.
32. Noels L, Radovitzky R. A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications. International Journal for Numerical Methods in Engineering 2006; 68:64-97.
33. Ten Eyck A, Lew A. Discontinuous Galerkin methods for non-linear elasticity. International Journal for Numerical Methods in Engineering 2006; 67:1204-1243.
34. Hansbo P, Hermansson J, Svedberg T. Nitsche's method combined with space-time finite elements for ALE fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 2004; 193: 4195-4206.
35. Hansbo P, Hermansson J. Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems. Computational Mechanics 2003; 32:134-139.
36. Chessa J, Belytschko T. A local space-time discontinuous finite element method. Computer Methods in Applied Mechanics and Engineering 2006; 195:1325-1343.
37. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua Structures. Wiley: New York, 2001.
38. Belytschko T, Parimi C, Moës N, Sukumar N, Usui S. Structured extended finite element methods for solids defined by implicit surfaces. International Journal for Numerical Methods in Engineering 2003; 56:609-635.
39. Ventura G, Moran B, Belytschko T. Dislocations by partition of unity. International Journal for Numerical Methods in Engineering 2005; 62:1463-1487.