Immersed smoothed finite element method for two dimensional fluid-structure interaction problems

International Journal for Numerical Methods in Engineering

Volumn 90, Issue 10, 2012, Pages 1292-1320

  Zhang, Zhi Qian ^a   Liu, G R ^b   Khoo, Boo Cheong ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b 705 Engineering Research Center   (United States)

Author keywords

Characteristic based split; Fluid structure interaction; Immersed boundary; Smoothed finite element method

Indexed keywords

CHARACTERISTIC-BASED SPLIT; CONVERGENCE PROPERTIES; EXPLICIT TIME INTEGRATION; FLUID-STRUCTURE INTERACTION PROBLEM; IMMERSED BOUNDARY; INCOMPRESSIBLE VISCOUS FLUIDS; MESH SIZE; NONLINEAR SOLIDS; NUMERICAL EXAMPLE; SEMI-IMPLICIT; SMOOTHED FINITE ELEMENT METHOD; TRIANGULAR ELEMENTS; VOLUME CORRECTION;

FINITE ELEMENT METHOD; TWO DIMENSIONAL;

FLUID STRUCTURE INTERACTION;

EID: 84861200205     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4299     Document Type: Article

References (44)

1. Peskin CS. Numerical analysis of blood flow in the heart. Journal of Computational Physics 1977 25(3): 220-252. DOI: 10.1016/0021-9991(77)90100-0.
2. Peskin CS. The immersed boundary method. Acta Numerica 2002 11: 479-517. DOI: 10.1017/S0962492902000077.
3. Mohd-Yusof J (ed). Combined Immersed-boundary/b-Spline Methods for Simulations of Flow in Complex Geometries, CTR Annual Research Briefs, NASA Ames Research Center/Stanford Univ. Center for Turbulence Research: Stanford, CA, 1997.
4. Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics 2000 161(1): 35-60. DOI: 10.1006/jcph.2000.6484.
5. Gilmanov A, Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. Journal of Computational Physics 2005 207(2): 457-492. DOI: 10.1016/j.jcp.2005.01.020.
6. Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics 2005 209(2): 448-476. DOI: 10.1016/j.jcp.2005.03.017.
7. Glowinski R, Pan T-W, Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1994 112(1-4): 133-148. DOI: 10.1016/0045-7825(94)90022-1.
8. 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. DOI: 10.1016/j.cma.2003.12.044.
9. Liu WK, Liu Y, Farrell D, Zhang L, Wang XS, Fukui Y, Patankar N, Zhang Y, Bajaj C, Lee J, Hong J, Chen X, Hsu H. Immersed finite element method and its applications to biological systems.Computer Methods in Applied Mechanics and Engineering 2006 195(13-16): 1722-1749. DOI: 10.1016/j.cma.2005.05.049.
10. Zhang LT, Gay M. Immersed finite element method for fluid-structure interactions.Journal of Fluids and Structures 2007 23(6): 839-857. DOI: 10.1016/j.jfluidstructs.2007.01.001.
11. Lee TR, Chang YS, Choi JB, Kim DW, Liu WK, Kim YJ. Immersed finite element method for rigid body motions in the incompressible Navier-Stokes flow. Computer Methods in Applied Mechanics and Engineering 2008 197(25-28): 2305-2316. DOI: 10.1016/j.cma.2007.12.013.
12. Wang XS, Zhang LT. Interpolation functions in the immersed boundary and finite element methods. Computational Mechanics 2010 45(4): 321-334. DOI: 10.1007/s00466-009-0449-5.
13. Bao Y, Zhou D, Zhao YJ. A two-step Taylor-characteristic-based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles. International Journal for Numerical Methods in Fluids 2010 62(11): 1181-1208. DOI: 10.1002/fld.2054.
14. Zhang ZQ, Liu GR. An immersed smoothed finite element method for fluid-structure interaction problems. International Journal of Computational Methods 2011 8(4): 747-757. DOI: 10.1142/S0219876211002794.
15. Löhner R. Applied Computational Fluid Dynamics Techniques : An Introduction Based on Finite Element Methods, 2 ed. John Wiley & Sons Ltd: Chichester, 2008.
16. Hughes TJR, Franca LP, Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the babuska-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 1986 59(1): 85-99. DOI: 10.1016/0045-7825(86)90025-3.
17. Tezduyar TE, Mittal S, Ray SE, Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Computer Methods in Applied Mechanics and Engineering 1992 95(2): 221-242. DOI: 10.1016/0045-7825(92)90141-6.
18. Tezduyar TE. Stabilized finite-element formulations for incompressible-flow computations. Advances in Applied Mechanics, Vol 28 1992 28: 1-44.
19. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982 32(1-3): 199-259. DOI: 10.1016/0045-7825(82)90071-8.
20. Donea J. A Taylor-Galerkin method for convective-transport problems.International Journal for Numerical Methods in Engineering 1984 20(1): 101-119. DOI: 10.1002/nme.1620200108.
21. Zienkiewicz OC, Taylor RL. The Finite Element Method, 5 ed. Fluid dynamics, vol. 3, Butterworth-Heinemann: Oxford, 2000.
22. Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P. The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems. International Journal for Numerical Methods in Fluids 1999 31(1): 359-392. DOI: 10.1002/(sici)1097-0363(19990915)31:1<359::aid-fld984>3.0.co;2-7.
23. Tezduyar TE. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 2001 8(2): 83-130. DOI: 10.1007/bf02897870.
24. Liu GR, Nguyen-Thoi T, Lam KY. An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. Journal of Sound and Vibration 2009 320(4-5): 1100-1130. DOI: 10.1016/j.jsv.2008.08.027.
25. Liu GR, Nguyen-Thoi T. Smoothed Finite Element Method, CRC Press: Boca Raton, 2010.
26. Liu GR, Liu MB. Smoothed Particle Hydrodynamics: A Meshfree Particle Method, World Scientific Publishing Company: Singapore, 2003.
27. Liu GR, Quek SS. The Finite Element Method : A Practical Course, Butterworth-Heinemann: Oxford, 2003.
28. Tang LM, Chen WJ, Liu XY.1983. String net function approximation and quasi-conforming technique, In Hybrid and Mixed Finite Element Methods, Atluri SN, Gallagher RH, Zienkiewicz OC (eds), John Wiley & Sons, Chichester.
29. Chen J-S, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001 50(2): 435-466. DOI: 10.1002/nme.338.
30. Liu GR. A G space theory and a weakened weak (W-2) form for a unified formulation of compatible and incompatible methods: Part I theory. International Journal for Numerical Methods in Engineering 2010 81(9): 1093-1126. DOI: 10.1002/nme.2719.
31. Liu GR. A G space theory and a weakened weak (W-2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems.International Journal for Numerical Methods in Engineering 2010 81(9): 1127-1156. DOI: 10.1002/nme.2720.
32. Liu GR. Mesh Free Methods: Moving Beyond the Finite Element Methods, 2 ed. CRC Press: Boca Raton, 2009.
33. Lai MC, Peskin CS. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. Journal of Computational Physics 2000 160(2): 705-719. DOI: 10.1006/jcph.2000.6483.
34. Liao CC, Chang YW, Lin CA, McDonough JM. Simulating flows with moving rigid boundary using immersed-boundary method. Computers & Fluids 2010 39(1): 152-167. DOI: 10.1016/j.compfluid.2009.07.011.
35. Su SW, Lai MC, Lin CA. An immersed boundary technique for simulating complex flows with rigid boundary. Computers & Fluids 2007 36(2): 313-324. DOI: 10.1016/j.compfluid.2005.09.004.
36. Beyer RP, Leveque RJ. Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Anal. 1992 29(2): 332-364. DOI: 10.1137/0729022.
37. Massarotti N, Arpino F, Lewis RW, Nithiarasu P. Explicit and semi-implicit CBS procedures for incompressible viscous flows. International Journal for Numerical Methods in Engineering 2006 66(10): 1618-1640. DOI: 10.1002/nme.1700.
38. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons: Chichester, 2000.
39. Peskin CS. Flow patterns around heart valves: A numerical method. Journal of Computational Physics 1972 10(2): 252-271. DOI: 10.1016/0021-9991(72)90065-4.
40. Boffi D, Gastaldi L, Heltai L. On the CFL condition for the finite element immersed boundary method. Computers & Structures 2007 85(11-14): 775-783. DOI: 10.1016/j.compstruc.2007.01.009.
41. Dunne T. An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaptation. International Journal for Numerical Methods in Fluids 2006 51(9-10): 1017-1039. DOI: 10.1002/fld.1205.
42. Zhao H, Freund JB, Moser RD. A fixed-mesh method for incompressible flow-structure systems with finite solid deformations. Journal of Computational Physics 2008 227(6): 3114-3140. DOI: 10.1016/j.jcp.2007.11.019.
43. Hirt CW, Amsden AA, Cook JL. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 1997 135(2): 203-216. DOI: 10.1006/jcph.1997.5702.
44. Clift R, Grace JR, Weber ME. Bubbles, Drops, and Particles, Academic Press: New York, 1978.