Hostname: page-component-7b9c58cd5d-dlb68 Total loading time: 0 Render date: 2025-03-14T12:54:32.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Methods for Fluid-Structure Interaction — A Review

Published online by Cambridge University Press:  20 August 2015

Gene Hou ,
Jin Wang  and
Anita Layton
Gene Hou*
Affiliation:
Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA 23529, USA
Jin Wang*
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Anita Layton*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708, USA
*
Email:ghou@odu.edu
Corresponding author.Email:j3wang@odu.edu
Email:alayton@math.duke.edu

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and non-conforming meshes that are currently available for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions.

Keywords

65-0265Z0574F10Fluid-structure interactionconforming and non-conforming meshesimmersed methods
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 2 , August 2012 , pp. 337 - 377
Copyright
Copyright © Global Science Press Limited 2012

References

[1] ANSYS web page: www.ansys.com.Google Scholar
[2]Appa, K., Finite-Surface Spline, Journal of Aircraft, Vol. 26, No.5, 1989, pp. 495–496.Google Scholar
[3]Badia, S., Nobile, F., and Vergara, C., Fluid-structure partitioned procedures based on robin transmission conditions, Journal of Computational Physics, Vol. 227, 2008, pp. 7027–7051.Google Scholar
[4]Bathe, K. J., Nitikitpaiboon, C. and Wang, X., A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers &Structures, Vol. 56, 1995, pp. 225–237.CrossRefGoogle Scholar
[5]Beale, J. T. and Layton, A. T., On the accuracy of finite difference methods for elliptic problems with interfaces, Communications in Applied Mathematics and Computational Sciences, Vol. 1, 2006, pp. 91–119.Google Scholar
[6]Beale, J. T. and Layton, A. T., A velocity decomposition approach for moving interfaces in viscous fluids, Journal of Computational Physics, Vol. 228, 2009, pp. 3358–3367.CrossRefGoogle Scholar
[7]Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P., Meshless methods: An overview and recent developments, Computer Methods in Applied Mechanics and Engineering, Vol. 139, 1996, pp. 3–47.Google Scholar
[8]Berthelsen, P. A. and Faltinsen, O. M., A local directional ghost cell approach for incompressible viscous flow problems with irregular boundaries, Journal of Computational Physics, Vol. 227, 2008, pp. 4354–4397.CrossRefGoogle Scholar
[9]Beyer, R. P., A computational model of the cochlea using the immersed boundary methods, Journal of Computational Physics, Vol. 98, 1992, pp. 145–162.Google Scholar
[10]Blake, J., Fluid mechanics of cilliary propulsion, Computational Modeling in Biological Fluid Dynamics (Eds. Fauci, and Gueron, ), Springer-Verlag: NY, 1999.Google Scholar
[11]Brown, S. A., Displacement Extrapolations for CFD+CSM Aeroelastic Analysis, AIAA-97-1090, presented at the 38th AIAA/ASME/ASCE/AHAIASC, Structures, Structural Dynamics and Materials, 1997, pp. 291–300.CrossRefGoogle Scholar
[12]Byun, C. and Guruswamy, G. P., Static Aeroelasticity Computations for Flexible 6th Wing-Body-Control Configurations, AIAA-96-4059, presented at the AlAA/ USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 4-6, 1996, pp. 744–754.Google Scholar
[13]Causin, P., Gerbeau, J. F. and Nobile, F., Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Computer Methods in Applied Mechanics and Engineering, Vol. 194, 2005, pp. 4506–4527.CrossRefGoogle Scholar
[14]Cebral, J. R. and Lohner, R, Conservative load projection and tracking for fluid-structure problems, AIAA Journal, Vol. 35, No.4, 1997, pp. 687–691.Google Scholar
[15]Cebral, J. R and Lohner, R, Fluid-Structure Coupling: Extensions and Improvements, AIAA-97-0858, presented at the 35th Aerospace Sciences Meeting & Exhibit, Reno, NV, January 6-9, 1997.Google Scholar
[16]Ceniceros, H. D., Fisher, J. E., and Roma, A. M., Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method, Journal of Computational Physics, Vol. 228, 2009, pp. 7137–7158.Google Scholar
[17]Chakrabarti, S. K. (Ed.), Numerical Models in Fluid Structure Interaction, Advances in Fluid Mechanics, Vol. 42, WIT Press, 2005.Google Scholar
[18]Cortez, R. and Minion, M. L., The blob projection method for immersed boundary problems, Journal of Computational Physics, Vol. 161, 2000, pp. 428–453.Google Scholar
[19]Degroote, J., Bruggeman, P., Haelterman, R. and Vierendeels, J., Stability of a coupling technique for partitioned solvers in FSI applications, Computers and Structures, Vol. 86, 2008, pp. 2224–2234.Google Scholar
[20]de Tullion, M. D., De Palma, P., Iaccarino, G., Pascazio, G., and Napolitano, M., An immersed boundary method for compressible flows using local grid refinement, Journal of Computational Physics, Vol. 225, 2007, pp. 2098–2117.CrossRefGoogle Scholar
[21]Dillon, R., Fauci, L. and Gaver, D. III, A microscale model of bacterial swimming, chemotaxis, and substrate transport, Journal of Theoretical Biology, Vol. 177, 1995, pp. 325–340.Google Scholar
[22]Dolbow, J., Moés, N. and Belytschko, T., An extended finite element method for modeling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering, Vol. 190, 2001, pp. 6825–6846.Google Scholar
[23]Dowell, E. H. and Hall, K. C., Modeling of fluid-structure interaction, Annual Review of Fluid Mechanics, Vol. 33, 2001, pp. 445–490.CrossRefGoogle Scholar
[24]Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, Journal of Computational Physics, Vol. 161, 2000, pp. 35–60.Google Scholar
[25]Fauci, L. J. and Folgelson, A. L., Truncated newton methods and the modeling of complex immersed elastic structures, Communications in Pure and Applied Mathematics, Vol. 66, 1993, pp. 787–818.Google Scholar
[26]Fauci, L. and A., McDonald, Sperm mobility in the presence of boundaries, Bulletin of Mathematical Biology, Vol. 57, 1995, 679–699.CrossRefGoogle ScholarPubMed
[27]Farhat, C., van der Zee, K. G. and Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Computer Methods in Applied Mechanics and Engineering, Vol. 195, 2006, pp. 1973–2001.CrossRefGoogle Scholar
[28]Farhat, C., Lesoinne, M. and LeTallec, P, Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity, Computer Methods in Applied Mechanics and Engineering, Vol. 157, 1998, pp. 95–114.Google Scholar
[29]Ghias, R., Mittal, R. and Lund, T. S., A non-body conformal grid method for simulation of compressible flows with complex immersed boundaries, AIAA paper 2004-0080.Google Scholar
[30]Glowinski, R., Pan, T.-W., Hesla, T. I., and Joseph, D. D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, International Journal of Multiphase Flow, Vol. 25, 1999, pp. 755–794.CrossRefGoogle Scholar
[31]Glowinski, R., Pan, T.-W., Hesla, T. I., Joseph, D. D., and Periaux, J., A distributed lagrange multiplier/fictitious domain method for the simulation of flows around moving rigid bodies: application to particulate flow, Computer Methods in Applied Mechanics and Engineering, Vol. 184, 2000, pp. 241–268.Google Scholar
[32]Glowinski, R., Pan, T.-W., Hesla, T. I., Joseph, D. D., and Periaux, 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, Vol. 169, 2001, pp. 363–427.Google Scholar
[33]Goldstein, D., Handler, R. and Sirovich, L., Modeling a no-slip flow boundary with an external force field, Journal of Computational Physics, Vol. 105, 1993, pp. 354–366.Google Scholar
[34]Griffith, B. E., Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 2005.Google Scholar
[35]Griffith, B. E. and Peskin, C. S., On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems, Journal of Computational Physics, Vol. 208, 2005, pp. 75–105.Google Scholar
[36]Grigoriadis, D. G. E., Kassinos, S. C. and Votyakov, E. V., Immersed boundary method for the MHD flows of liquid metals, Journal of Computational Physics, Vol. 228, 2009, pp. 903–920.Google Scholar
[37]Guruswamy, P. G. and Byun, C., Direct coupling of euler flow equations with plate finite element structures, AlAA Journal, Vol. 33, No.2, 1994, pp. 375–377.Google Scholar
[38]Guy, R. D. and Hartenstine, D. A., On the accuracy of direct forcing immersed boundary methods with projection methods, Journal of Computational Physics, Vol. 229, 2010, pp. 2479–2496.Google Scholar
[39]Haase, W., Unsteady Aerodynamics Including Fluid/Structure Interaction, Air and Space Europe, Vol. 3, 2001, pp. 83–86.Google Scholar
[40]Haug, E. J., Intermediate Dynamics, Prentice Hall, 1992.Google Scholar
[41]Hirt, C. W. and Nichols, B. D., Volume of fluid (VOF) method for dynamics of free boundaries, Journal of Computational Physics, Vol. 39, 1981, pp. 201–225.CrossRefGoogle Scholar
[42]Hoburg, J. F. and Melcher, J. R., Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients, Journal of Fluid Mechanics, Vol. 73, 1976, pp. 333–351.Google Scholar
[43]Hou, G., and Satyanarayana, A., Analytical Sensitivity Analysis of a Static Aeroelastic Wing, Proceedings of 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, Sept. 2000; Also AIAA Paper 2000-4824.Google Scholar
[44]Hou, T. Y., Lowengrub, J. S., and Shelley, M. J., Removing the stiffness from interfacial flows with surface tension., Journal of Computational Physics, Vol. 114, 1994, pp. 312–338.CrossRefGoogle Scholar
[45]Hou, T. Y. and Shi, Z., An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, Journal of Computational Physics, Vol. 227, 2008, pp. 8968–8991.Google Scholar
[46]Hou, T. Y. and Shi, Z., Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations, Journal of Computational Physics, Vol. 227, 2008, pp. 9138–9169.CrossRefGoogle Scholar
[47]Howe, M. S., Acoustics of Fluid-Structure Interactions, Cambridge University Press, 1998.CrossRefGoogle Scholar
[48]Huang, W. X. and Sung, H. J., An immersed boundary method for fluid-flexible structure interaction, Computer Methods in Applied Mechanics and Engineering, Vol. 198, 2009, pp. 2650–2661.CrossRefGoogle Scholar
[49]Hubner, B., Walhorn, E. and Dinkler, D., A monolithic approach to fluid-structure interaction using space-time finite elements, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 2087–2104.Google Scholar
[50]Iaccarino, G. and Verzicco, R., Immersed boundary technique for turbulent flow simulations, Applied Mechanics Review, Vol. 56, 2003, pp. 331–347.Google Scholar
[51]Idelsohn, S. R., Onate, E., Del Pin, F. and Calvo, N., Fluid-structure interaction using the particle finite element method, Computer Methodsin Applied Mechanics and Engineering, Vol. 195, 2006, pp. 2100–2123.CrossRefGoogle Scholar
[52]Idelsohn, S. R., Marti, J., Limache, A. and Onate, E., Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the PFEM, Computer Methods in Applied Mechanics and Engineering Vol. 197, 2008, pp. 1762–1776.Google Scholar
[53]Irons, B. and Tuck, R. C., A Version of the Aitken accelerator for computer implementation, International Journal for Numerical Methods in Engineering, Vol. 1, 1969, pp. 275–277.Google Scholar
[54]Jayathilake, P. G., Khoo, B. C. and Tan, Z., Effect of membrane permeability on capsule substrate adhesion: Computation using immersed interface method, Chemical Engineering Science, Vol. 65, 2010, pp. 3567–3578.Google Scholar
[55]Kaligzin, G. and Iaccarino, G., Toward immersed boundary simulation of high Reynolds number flows, Annual Research Briefs, Center for Turbulence Research, Stanford University, 2003, pp. 369–378.Google Scholar
[56]Kapania, R. K., Bhardwaj, M. K., Reichenbach, E. and Guruswamy, G. P., Aeroe-lastic Analysis of Modern Complex Wings, AIAA-96-38728, presented at the 6th AlAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 4-6, 1996, pp. 258–265.CrossRefGoogle Scholar
[57]Kim, D. and Choi, H., Immersed boundary method for flow around an arbitrarily moving body, Journal of Computational Physics, Vol. 212, 2006, pp. 662–680.Google Scholar
[58]Kim, J., Kim, D. and Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, Journal of Computational Physics, Vol. 171, 2001, pp. 132–150.CrossRefGoogle Scholar
[59]Kim, Y. and Peskin, C. S., Penalty immersed boundary method for an elastic boundary with mass, Physics of Fluids, Vol. 19, 053103, 2007, pp. 1–18.Google Scholar
[60]Kropinski, M. C. A., An efficient numerical method for studying interfacial motion in two-dimensional creeping flows, Journal of Computational Physics, Vol. 171, 2001, pp. 479–508.Google Scholar
[61]Lallemand, P. and Luo, L.-S., Lattice Boltzmann method for moving boundaries, Journal of Computational Physics, Vol. 184, 2003, pp. 406–421.CrossRefGoogle Scholar
[62]Layton, A. T., Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces, Computer and Fluids, Vol. 38, 2009, pp. 266–272.Google Scholar
[63]Layton, A. T., and Beale, J. T., A partially implicit hybrid method for computing interface motion in Stokes flow, Discrete and Continuous Dynamical Systems B, 2010, submitted.Google Scholar
[64]Le, D. V., Khoo, B. C. and Lim, K. M., An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 2119–2130.Google Scholar
[65]Lee, T. R., Chang, Y. S., Choi, J. B., Kim, D. W., Liu, W. K. and Kim, Y. J., Immersed finite element method for rigid body motions in the incompressible Navier-Stokes flow, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 2305–2316.Google Scholar
[66]Lefranc¸ois, E. and Boufflet, J.-P., An Introduction to Fluid-Structure Interaction: Application to the Piston Problem, SIAM Review, Vol. 52, 2010, pp. 747–767.Google Scholar
[67]Leveque, R. J. and Li, Z., Immersed interface method for Stokes flow with elastic boundaries or surface tension, SIAM Journal on Scientific Computing, Vol. 18, 1997, 709-735.Google Scholar
[68]Lee, L. and R. J., LeVeque, An immersed interface method for the incompressible Navier-Stokes equations, SIAM Journal on Scientific Computing, Vol. 25, 2003, pp. 832–856.Google Scholar
[69]Li, Z., An overview of the immersed interface method and its applications, Taiwanese Journal of Mathematics, Vol. 7(1), 2003, pp. 1–49.Google Scholar
[70]Li, Z. and Ito, K., The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, Society for Industrial and Applied Mathematic, 2006.Google Scholar
[71]Li, Z., Ito, K. and Lai, M.-C., An augmented approach for Stokes equations with a discontinuous viscosity and singular forces, Computers &Fluids, Vol. 36, 2007, pp. 622–635.Google Scholar
[72]Li, Z. and Lai, M. C., The immersed interface method for the Navier-Stokes equations with singular forces, Journal of Computational Physics, Vol. 171, 2001, pp. 822–842.CrossRefGoogle Scholar
[73]Li, Z., Lai, M.-C., He, G. and Zhao, H., An augmented method for free boundary problems with moving contact lines, Computers &Fluids, Vol. 39, 2010, pp. 1033–1040.Google Scholar
[74]Liu, W. K., Kim, D. W. and Tang, S., Mathematical foundations of the immersed finite element method, Computational Mechanics, Vol. 39, 2006, pp. 211–222.Google Scholar
[75]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, Vol. 195, 2006, pp. 1722–1749.Google Scholar
[76]Luo, K., Wang, Z. and Fan, J., A modified immersed boundary method for simulation of fluid-particle interactions, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2007, pp. 36–46.CrossRefGoogle Scholar
[77]Mark, A. and van Wachem, B. G. M., Derivation and validation of a novel implicit second-order accurate immersed boundary method, Journal of Computational Physics, Vol. 227, 2008, pp. 6660–6680.Google Scholar
[78]Mayo, A. and Peskin, C. S., An implicit numerical method for fluid dynamics problems with immersed elastic boundaries, in Fluid Dynamics in Biology (Ed. Cheer, A. Y. and von Dam, C. P.), pp. 261–278, Providence, RI, 1993, AMS.Google Scholar
[79]S., Mönkölä, Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements, Journal of Computational and Applied Mathematics, Vol. 234, 2010, pp. 1904–1911.Google Scholar
[80]Michler, C., Hulshoff, S. J., van Brummelen, E. H. and de Borst, R., A monolithic approach to fluid-structure interaction, Computers &Fluids, Vol. 33, 2004, pp. 839–848.Google Scholar
[81]Mittal, R. and Iaccarino, G., Immersed boundary methods, Annual Review of Fluid Mechanics, Vol. 37, 2005, pp. 239–261.Google Scholar
[82]Mittal, R., Dong, H., Bozkurttas, M and Najjar, F. M., A versatile sharp interface immersed boundary method for incompressible flow with complex boundaries, Journal of Computational Physics, Vol. 227, 2008, pp. 4825–4852.Google Scholar
[83]Moés, N., Dolbow, J. and Belytschko, T., A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, Vol. 46, 1999, pp. 131–150.Google Scholar
[84]J., Mohd-Yusof, Combined immersed boundary/B-spline methods for simulations of flow in complex geometries, Annual Research Briefs, Center for Turbulence Research, Stanford University, 1999, pp. 317–327.Google Scholar
[85]Morand, H. J.-P. and Ohayon, R., Fluid-Structure Interaction: Applied Numerical Methods, Wiley, 1995.Google Scholar
[86]Mori, Y. and Peskin, C. S., Implicit second order immersed boundary methods with boundary mass., Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 2049–2067.Google Scholar
[87]Mucha, P. J., Tee, S. Y., Weitz, D. A., Shraiman, B. I. and Brenner, M. P., A model for velocity fluctuations in sedimentation, Journal of Fluid Mechanics, Vol. 501, 2004, pp. 71–104.Google Scholar
[88]Newren, E., Fogelson, A., Guy, R., and Kirby, M., A comparison of implicit solvers for the immersed boundary equations, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 2290–2304.Google Scholar
[89]Newman, J. c. III, Newman, P. A., Taylor, A. C. III, and Hou, G. J.-W., Efficient non-linear static aeroelastic wing analysis, International Journal of Computers and Fluids, Vol. 28, January 1999, pp. 615–628.Google Scholar
[90]Nocedal, J. and Wright, S. J., Numerical Optimization, Springer, 1999.CrossRefGoogle Scholar
[91]Onishi, RKimura, TGuo, Z. and Iwamiya, T, Coupled Aero-Structural Model: Approach and Application to High Aspect-Ratio Wing-Box Structures, AIAA-98-4837, presented at the 7th AIAAlUSAFINASA/ISSMO Symposium on Multidisci-plinary Analysis and Optimization, St. Louis, MO, September 2-4, 1998, pp. 1004–1010.Google Scholar
[92]Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, Vol. 79, 1988, pp. 12–49.Google Scholar
[93]Owen, D. R. J., Leonardi, C. R. and Feng, Y. T., An efficient framework for fluid-structure interaction using the lattice Boltzmann method and immersed moving boundaries, International Journal for Numerical Methods in Engineering, 2010, in press (DOI: 10.1002/nme.2985).Google Scholar
[94]Paik, K. J., Simulation of fluid-structure interaction for surface ships with linear/nonlinear deformations, Ph.D.Thesis, The University of Iowa, 2010.Google Scholar
[95]Patankar, N. A., A Formulation for Fast Computations of Rigid Particulate Flows, Center for Turbulence Research, Annual Research Briefs, 2001, pp. 1–19.Google Scholar
[96]Peskin, C. S., Numerical analysis of blood flow in the heart, Journal of Computational Physics, Vol. 25, 1977, pp. 220–252.CrossRefGoogle Scholar
[97]Peskin, C. S., The immersed boundary method, Acta Numerica, Vol. 11, 2002, pp. 479–517.Google Scholar
[98]Peskin, C. S. and Printz, B. F., Improved volume conservation in the computation of flows with immersed elastic boundaries, Journal of Computational Physics, Vol. 105, 1993, pp. 33–46.Google Scholar
[99]Ramiere, I., Angot, P. and Belliard, M., A general ficitious domain method with immersed jumps and multilevel nested structured meshes, Journal of Computational Physics, Vol. 225, 2007, pp. 1347–1387.Google Scholar
[100]Raveh, D. E. and Karpel, M., Structural Optimization of Flight Vehicles with Non-linear Aerodynamic Loads, AIAA-98-4832, presented at the 7th AIAA/USAF/NASA/ ISSMO Symposium ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, September 2-4, 1998, pp. 967–977.Google Scholar
[101]Roma, A. M., Peskin, C. S. and Berger, M. J., An adaptive version of the immersed boundary method, Journal of Computational Physics, Vol. 153, 1999, pp. 509–534.Google Scholar
[102]Ross, M. R., Coupling and simulation of acoustic fluid-structure interaction systems using localized Lagrange multipliers, Ph.D. Thesis, University of Colorado at Boulder, 2006.Google Scholar
[103]Ryzhakov, P. B., Rossi, R., Idelsohn, S. R. and Oñate, E., A monolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, Vol. 46, 2010, pp. 883–899.Google Scholar
[104]Samareh, J. A., Use of CAD Geometry in MDO, AIAA-96-3991, presented at the 6th AIAAlUSAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 4-6, 1996.Google Scholar
[105]Samareh, J. A., Aeroelastic Deflection of NURBS Geometry, presented at the 6th International Conference on Numerical Grid Generation in Computational Field Simulation, University of Greenwhich, Avery Hill Campus, London, UK, July 6-9, 1998, pp. 727–736.Google Scholar
[106]Samareh, J. A., A Novel Shape Parameterization Approach, NASA Contract No. TM-1999-209116, NASA Langley Research Center, Hampton, VA 23681-2199, May 1999.Google Scholar
[107]Samareh, J. A., A Survey of Shape Parameterization Techniques, presented at the AIANCEASIICASEINASA-LaRCInternational Forum on Aeroelasticity and Structural Dynamics, Williamsburg, VA, June 22-25, 1999, pp. 333–343.Google Scholar
[108]Samareh, J. A., Status and future of geometry modeling and grid generation for design and optimization, Journal of Aircraft, Vol. 36, No. I, 1999, pp. 97–104.Google Scholar
[109]Sanders, J., Dolbow, J. E., Mucha, P. J. and Laursen, T. A., A new method for simulating rigid body motion in incompressible two-phase flow, International Journal for Numerical Methods in Fluids, 2010, in press (DOI: 10.1002/fld.2385).Google Scholar
[110]Shen, L. and Chan, E-S, Numerical simulation of fluid-structure interaction using a combined volume of fluid and immersed boundary method, Ocean Engineering, Vol. 35, 2008, pp. 939–952.Google Scholar
[111]Shyy, W., Udaykumar, H. S., Rao, M. M. and Smith, R. W., Computational Fluid Dynamics with Moving Boundaries, Dover Publications, 2007.Google Scholar
[112]Sohn, J. S., Tseng, Y.-H., Li, S., Voigt, A., and Lowengrub, J. S., Dynamics of multicom-ponent vesicles in a viscous fluid, Journal of Computational Physics, Vol. 229, 2010, pp. 119–144.Google Scholar
[113]Souli, M. and Benson, D. J. (Ed.), Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction: Numerical Simulation, Wiley-ISTE, 2010.Google Scholar
[114]Stockie, J. M., and Green, S. I., Simulating the motion of flexible pulp fibres using the immersed boundary method, Journal of Computational Physics, Vol. 147, 1998, pp. 147–165.Google Scholar
[115]Stockie, J. M. and Wetton, B. R., Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes, Journal of Computational Physics, Vol. 154, 1999, pp. 41–64.Google Scholar
[116]Tai, C. H., Liew, K. M. and Zhao, Y., Numerical simulation of 3D fluid-structure interaction flow using an immersed object method with overlapping grids, Computers and Structures, Vol. 85, 2007, pp. 749–762.Google Scholar
[117]Tai, C. H., Zhao, Y. and Liew, K. M., Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids, Journal of Computational Physics, Vol. 207, 2005, pp. 151–172.Google Scholar
[118]Taira, K. and Colonius, T., The immersed boundary method: A project approach, Journal of Computational Physics, Vol. 225, 2007, pp. 2118–2137.Google Scholar
[119]Tan, Z., Le, D. V., Lim, K. M. and Khoo, B. C., An immersed interface method for the incompressible Navier-Stokes equations with discontinuous viscosity across the interface, SIAM Journal on Scientific Computing, Vol. 31, 2009, pp. 1798–1819.Google Scholar
[120]Tan, Z., Lim, K. M. and Khoo, B. C., An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries, Journal of Computational Physics, Vol. 228, 2009, pp. 6855–6881.Google Scholar
[121]Tornberg, A.-K. and Engquist, B., Numerical approximations of singular source terms in differential equations, Journal of Computational Physics, Vol. 200, 2004, pp. 462–488.Google Scholar
[122]Tornberg, A.-K. and Shelley, M. J., Simulating the dynamics and interactions of flexible fibers in Stokes flow, Journal of Computational Physics, Vol. 196, 2004, pp. 8–40.Google Scholar
[123]Tseng, Y.-H. and Ferziger, J. H., A ghost-cell immersed boundary method for flow in complex geometry, Journal of Computational Physics, Vol. 192, 2003, pp. 593–623.Google Scholar
[124]Tu, C. and Peskin, C. S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods, SIAM Journal on Scientific and Statistical Computing, Vol. 13, 1992, pp. 1361–1376.Google Scholar
[125]Tzong, G., Chen, H. H., Chang, K. C., Wu, T and Cebeci, T, A General Method for Calculating Aero-Structure Interaction on Aircraft Configurations, AIAA-96-38704, presented at the 6th AIAAlUSAFINASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 4-6, 1996, pp. 14–24.Google Scholar
[126]Udaykumar, H. S., Mittal, R. and Shyy, W., Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids, Journal of Computational Physics, Vol. 153, 1999, pp. 534–574.Google Scholar
[127]Udaykumar, H. S., Mittal, R., Rampunggoon, P., Khanna, A., A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, Journal of Computational Physics, Vol. 174, 2001, pp. 345–380.Google Scholar
[128]Udaykumar, H. S., Shyy, W. and Rao, M. M., ELAFINT: A mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries, International Journal for Numerical Methods in Fluids, Vol. 22, 1996, pp. 691–705.Google Scholar
[129]Veerapaneni, S. K., Gueyffier, D., Zorin, D., and Biros, G., A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics, Vol. 228, 2009, pp. 2334–2353.Google Scholar
[130]Vierendeels, J., Dumont, K. and Verdonck, P. R., A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics, Journal of Computational and Applied Mathematics, Vol. 215, 2008, pp. 602–609.Google Scholar
[131]Wachs, A., Numerical simulation of steady bingham flow through an eccentric annular cross-section by distributed Lagrange multiplier/fictitious domain and augmented La-grangian methods, Journal of Non-Newtonian Fluid Mechanics, Vol. 142, 2007, pp. 183–198.Google Scholar
[132]Wall, W. A., Gerstenberger, A., Meayer, U. and Küttler, U., Advanced approaches for fluid-shell interaction, Proceedings of the 6th International Conference on Computation of Shell and Spatial Strucutres IASS-IACM, USA, 2008, pp. CD/ F-2-C.Google Scholar
[133]Wang, J. and Layton, A., Numerical simulations of fiber sedimentation in Navier-Stokes flows, Communications in Computational Physics, Vol. 5, No. 1, 2009, pp. 61–83.Google Scholar
[134]Wang, X. S., From immersed boundary method to immersed continuum method, International Journal for Multiscale Computational Engineering, Vol. 4, No. 1, 2006, pp. 127–145.Google Scholar
[135]Wang, X. S., An iterative matrix-free method in implicit immersed boundary/continuum method, Computers and Structures, Vol. 85, 2007, pp. 739–748.Google Scholar
[136]Wang, X. S., Immersed boundary/continuum methods, in Computational Modeling in Biomechanics, De, S.et al. (Eds.), Springer, 2010, pp. 3–48.Google Scholar
[137]Wang, X. S. and Liu, W. K., Extended immersed boundary method using FEM and RKPM, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 1305–1321.Google Scholar
[138]Wang, X. S., Zhang, L. T. and Liu, W. K., On computational issues of immersed finite element methods, Journal of Computational Physics, Vol. 228, 2009, pp. 2535–2551.Google Scholar
[139]Weymouth, G., Physics and Learning Based Computational Models for Breaking Bow Waves Based on New Boundary Immersion Approaches, Ph.D. Dissertation, MIT, 2008.Google Scholar
[140]Weymouth, G., Dommermuth, D. G., Hendrickson, K. and Yue, D. K.-P., Advances in Cartesian-grid Methods for Computational Ship Hydrodynamics, 26th Symposium on Naval Hydrodynamics, Rome, Italy, 17-22 September 2006.Google Scholar
[141]Wood, C., Gil, A. J., Hassan, O. and Bonet, J., Partitioned block-gauss-seidel coupling for dynamic fluid-structure interaction, Computers and Structures, Vol. 88, 2010, pp. 1367–1382.Google Scholar
[142]Xu, S. and Wang, Z. J., A 3D immersed interface method for fluid-solid interaction, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 2068–2086.Google Scholar
[143]Yang, J. and Balaras, E., An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, Journal of Computational Physics, Vol. 215, 2006, pp. 12–40.Google Scholar
[144]Ye, T., Mittal, R., Udaykumar, H. S. and Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, Journal of Computational Physics, Vol. 156, 1999, pp. 209–240.Google Scholar
[145]Yu, Z., A DLM/FD method for fluid/flexible-body interactions, Journal of Computational Physics, Vol. 207, 2005, pp. 1–27.Google Scholar
[146]Yu, Z. and Shao, X., A direct-forcing fictitious domain method for particulate flows, Journal of Computational Physics, Vol. 227, 2007, pp. 292–314.Google Scholar
[147]Zhang, L. T., Gerstenberger, A., Wang, X. and Liu, W. K., Immersed finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 2051–2067.Google Scholar
[148]Zhang, L. T. and Gay, M., Immersed finite element method for fluid-structure interactions, Journal of Fluids and Structures, Vol. 23, No. 6, 2007, pp. 839–857.Google Scholar
[149]Zhang, L. T., Wagner, G. J. and Liu, W. K., Modeling and simulation of fluid structure interaction by meshfree and FEM, Communications in Numerical Methods in Engineering, Vol. 19, 2003, pp. 615–621.Google Scholar
[150]Zhang, W., Jiang, Y. and Ye, Z., Two better loosely coupled solution algorithms of CFD based aeroelastic simulation, Engineering Applications of Computational Fluid Mechanics, Vol. 1, No. 4, 2007, pp. 253–262.Google Scholar
[151]Zhao, H., Freund, J. B. and Moser, R. D., A fixed-mesh method for incompressible flow-structure systems with finite solid deformation, Journal of Computational Physics, Vol. 227, 2008, pp. 3114–3140.Google Scholar