Erratum to "On computational issues of immersed finite element methods" [J. Comput. Phys. 228 (2009) 2535-2551] (DOI:10.1016/j.jcp.2008.12.012);On computational issues of immersed finite element methods

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2535-2551

  Sheldon Wang, X ^a   Zhang, L T ^b   Liu, Wing Kam ^c  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^c Northwestern University   (United States)

Author keywords

Driven cavity; Fluid structure interaction; Immersed boundary method; Immersed continuum method; Immersed finite element; Mixed finite element formulation

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MESH GENERATION; TURBULENT FLOW;

COMPUTATIONAL ISSUES; CONTINUUM METHOD; DRIVEN CAVITY; FINITE ELEMENT FORMULATIONS; FLUID-STRUCTURE INTERACTION; IMMERSED BOUNDARY METHODS; IMMERSED CONTINUUM METHOD; IMMERSED FINITE ELEMENT METHOD; IMMERSED FINITE ELEMENTS; MIXED FINITE ELEMENT FORMULATION;

FLUID STRUCTURE INTERACTION;

EID: 60149101432     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.05.041     Document Type: Erratum

References (35)

1. Bao W., Wang X., and Bathe K.J. On the Inf-Sup condition of mixed finite element formulations for acoustic fluids. Mathematical Models and Methods in Applied Sciences 11 (2001) 883-901
2. Boffi D., and Gastaldi L. A finite element approach for the immersed boundary method. Computers and Structures 81 (2003) 491-501
3. Boffi D., Gastaldi L., and Heltai L. On the CFL condition for the finite element immersed boundary method. Computers and Structures 85 (2007) 775-783
4. Boffi D., Gastaldi L., Heltai L., and Peskin C.S. On the hyperelastic formulation of the immersed boundary method. Computer Methods in Applied Mechanics and Engineering 197 (2008) 2210-2231
5. Chessa J., and Belytschko T. The extended finite element method for two-phase fluids. Journal of Applied Mechanics 70 (2003) 10-17
6. Peskin C.S. The immersed boundary method. Acta Numerica 11 (2002) 479-517
7. Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. Journal of Computational Physics 193 (2004) 357-397
8. Newren E.P., Fogelson A.L., Guy R.D., and Kirby R.M. Unconditionally stable discretizations of the immersed boundary equations. Journal of Computational Physics 222 (2007) 702-719
9. Gay M., Zhang L.T., and Liu W.K. Stent modeling using immersed finite element method. Computer Methods in Applied Mechanics and Engineering 195 (2005) 4358-4370
10. Wagner G.J., Moës N., Liu W.K., and Belytschko T.B. The extended finite element method for rigid particles in stokes flow. International Journal for Numerical Methods in Engineering 51 (2001) 293-313
11. Glowinski R., Pan T.W., Hesla T.I., Joseph D.D., and Périaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. Journal of Computational Physics 169 (2001) 363-426
12. Huerta A., and Liu W.K. Viscous flow with large free surface motion. Computer Methods in Applied Mechanics and Engineering 69 (1988) 277-324
13. Kay D., Loghin D., and Wathen A. A preconditioner for the steady-state Navier-Stokes equations. SIAM Journal on Scientific Computing 24 1 (2002) 237-256
14. Lim S., Ferent A., Wang X., and Peskin C.S. Dynamics of a closed rod with twist and bend in fluid. SIAM Journal on Scientific Computing 31 (2008) 273-302
15. Liu Y., Liu W.K., Belytschko T., Patankar N., To A.C., Kopacz A., and Chung J.H. Immersed electrokinetic finite element method. Computer Methods in Applied Mechanics and Engineering 71 (2007) 379-405
16. Tidriri M.D. Preconditioning techniques for the Newton-Krylov solution of compressible flows. Journal of Computational Physics 132 (1997) 51-61
17. Sulsky D., and Brackbill J.U. A numerical method for suspension flow. Journal of Computational Physics 96 (1991) 339-368
18. Sussman T., and Bathe K.J. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers and Structures 26 1/2 (1987) 357-409
19. Belytschko T. Fluid-structure interaction. Computers and Structures 12 (1980) 459-469
20. Tezduyar T.E. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 8 (2001) 83-130
21. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 59 (1986) 85-99
22. Van Loon R., Anderson P.D., Van de Vosse F.N., and Sherwin S.J. Comparison of various fluid-structure interaction methods for deformable bodies. Computers and Structures 85 (2006) 833-843
23. Wang X. From immersed boundary method to immersed continuum method. International Journal for Multiscale Computational Engineering 4 (2006) 127-145
24. Wang X. An iterative matrix-free method in implicit immersed boundary/continuum methods. Computers and Structures 85 (2007) 739-748
25. Wang X. Fundamentals of Fluid-Solid Interactions-Analytical and Computational Approaches (2008), Elsevier Science
26. Wang X., and Bathe K.J. Displacement/pressure based finite element formulations for acoustic fluid-structure interaction problems. International Journal for Numerical Methods in Engineering 40 (1997) 2001-2017
27. Wang X., and Liu W.K. Extended immersed boundary method using FEM and RKPM. Computer Methods in Applied Mechanics and Engineering 193 (2004) 1305-1321
28. Liu W.K., Kim D.W., and Tang S. Mathematical foundations of the immersed finite element method. Contemporary Mathematics 193 (2006) 1-12
29. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 20 (1995) 1081-1106
30. Liu W.K., Liu Y., Farrell D., Zhang L., Wang X., Fukui Y., Patankar N., Zhang Y., Bajaj C., Chen X., and Hsu H. Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering 195 (2006) 1722-1749
31. Liu W.K., and Ma D.C. Computer implementation aspects for fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 31 (1982) 129-148
32. Liu W.K., Belytschko T.B., and Chang H. An arbitrary Lagrangian-Eulerian finite element method for path-dependent materials. Computer Methods in Applied Mechanics and Engineering 58 (1986) 227-245
33. Yu Z. A DLM/FD method for fluid/flexible-body interactions. Journal of Computational Physics 207 (2005) 1-27
34. Zhang L., Gerstenberger A., Wang X., and Liu W.K. Immersed finite element method. Computer Methods in Applied Mechanics and Engineering 193 (2004) 2051-2067
35. Zhang L., Wagner G.J., and Liu W.K. Modeling and simulation of fluid structure interaction by meshfree and FEM. Communications in Numerical Methods in Engineering 19 (2003) 615-621