The fixed-mesh ALE approach applied to solid mechanics and fluid-structure interaction problems

International Journal for Numerical Methods in Engineering

Volumn 81, Issue 12, 2010, Pages 1529-1557

  Baiges, Joan ^a   Codina, Ramon ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

ALE formulations; Fixed mesh methods; Fluid structure interaction; Immersed boundaries

Indexed keywords

ALE FORMULATION; ALE METHODS; ARBITRARY LAGRANGIAN EULERIAN; DOMAIN BOUNDARY; FLUID-STRUCTURE INTERACTION PROBLEM; IMMERSED BOUNDARY; LAGRANGIAN APPROACHES; LARGE STRAINS; SOLID MECHANICS; SPATIAL DISCRETIZATIONS; TIME STEP;

COMPUTATIONAL FLUID DYNAMICS; FLUIDS; LAGRANGE MULTIPLIERS; MECHANICS; TURBULENT FLOW;

FLUID STRUCTURE INTERACTION;

EID: 75649141611     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2740     Document Type: Article

References (31)

1. Donea J, Fasoli-Stella P, Giuliani S. Lagrangian and Eulerian finite element techniques for transient fluid structure interaction problems. title typebookTransactions Fourth SMIRT/title, San Francisco, 1977; B1/2.
2. Huerta A, Liu WK. Viscous flow with large free surface motion. Computer Methods in Applied Mechanics and Engineering 1988; 69:277-324.
3. Hughes TJR, Liu WK, Zimmerman TK. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 1981; 29:329-349.
4. Codina R, Houzeaux G, Coppola-Owen H, Baiges J. The fixed-mesh ALE approach for the numerical approximation of flows in moving domains. Journal of Computational Physics 2009; 228:1591-1611.
5. Liu WK, Belytschko T, Chang H. An arbitrary Lagrangian-Eulerian finite element method for path-dependent materials. Computer Methods in Applied Mechanics and Engineering 1986; 58:227-245.
6. Benson DJ. An efficient, accurate, simple ALE method for nonlinear finite element programs. Computer Methods in Applied Mechanics and Engineering 1989; 72:305-350.
7. Ghosh S, Kikuchi N. An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids. Computer Methods in Applied Mechanics and Engineering 1991; 86:127-188.
8. Okazawa S, Kashiyama K, Kaneko Y. Eulerian formulation using stabilized finite element method for large dormation solid dynamics. International Journal for Numerical Methods in Engineering 2007; 72:1544-1559.
9. Peskin CS. Flow patterns around heart vales: a numerical method. Journal of Computational Physics 1972; 10:252-271.
10. Lai M-C, Peskin CS. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. Journal of Computational Physics 2000; 160:705-719.
11. LeVeque RJ, Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM Journal on Numerical Analysis 1994; 31(4):1019-1044.
12. LeVeque RJ, Li Z. Immersed interface method for incompressible Navier-Stokes equations. SIAM Journal on Scientific and Statistical Computing 1997; 18(3):709-735.
13. Xu S, Wang ZJ. An immersed interface method for simulating the interaction of a fluid with moving boundaries. Journal of Computational Physics 2006; 216:454-493.
14. Dolbow J, Mourad HM, Harari I. A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces. International Journal for Numerical Methods in Engineering 2007; 69:772-793.
15. Barbosa HJC, Hughes TJR. The finite element method with Lagrangian multipliers on the boundary: circumventing the Babuška-Brezzi condition. Computer Methods in Applied Mechanics and Engineering 1991; 85:109-128.
16. Ji H, Dolbow JE. 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.
17. Glowinski R, Pan T-W, Périaux J. A fictitious domain method for Dirichlet problems and applications. Computer Methods in Applied Mechanics and Engineering 1994; 111:203-303.
18. Glowinski R, Pan TW, Hesla TI, Joseph DD, Périaux J. A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: application to particulate flow. International Journal for Numerical Methods in Fluids 1999; 30:1043-1066.
19. 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.
20. Rodriguez-Ferran A, Casadei F, Huerta A. ALE stress update for transient and quasiestatic processes. International Journal for Numerical Methods in Engineering 1998; 43:241-262.
21. Newmark NM. A method of computation for structural dynamics. Journal of Engineering Mechanics Division (ASCE) 1959; 85:67-94.
22. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Computer Methods in Applied Mechanics and Engineering 1998; 156:185-210.
23. Hughes TJR. Multiscale phenomena: Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations. Computer Methods in Applied Mechanics and Engineering 1995; 127:387-401.
24. Huétink J. On the simulation of thermo-mechanical forming processes. Dissertation, 1986.
25. Armero F, Love E. An arbitrary Lagrangian-Eulerian finite element method for finite strain plasticity. International Journal for Numerical Methods in Engineering 2003; 57:471-508.
26. Coppola-Owen H, Codina R. A finite element model for free surface flows on fixed meshes. International Journal for Numerical Methods in Fluids 2007; 54:1151-1171.
27. Dunne T, Rannacher R. Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation. In Fluid-Structure Interaction: Modelling, Simulation, Optimisation, Bungartz HJ, Schäfer J (eds). Lecture Notes in Computational Science and Engineering, vol. 53. Springer: Heidelberg, 2006.
28. Codina R, Baiges J. Approximate imposition of boundary conditions in immersed boundary methods. International Journal for Numerical Methods in Engineering 2009; DOI: 10.1002/nme.2662.
29. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Computer Methods in Applied Mechanics and Engineering 2002; 191:4295-4321.
30. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2001.
31. Wall WA, Ramm E. Fluid-structure interaction based upon a stabilized (ALE) finite element method. In Proceedings of the Fourth World Congress on Computational Mechanics (WCCM IV), Oñate E, Idelsohn SR (eds), Buenos Aires, Argentina, 29 June-2 July 1998. CIMNE: Barcelona, 1998; 1988-1995.