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Numerical Methods for Fluid-Structure Interaction — A Review

  • Gene Hou (a1), Jin Wang (a2) and Anita Layton (a3)
Abstract
Abstract

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.

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Corresponding author
Email:ghou@odu.edu
Corresponding author.Email:j3wang@odu.edu
Email:alayton@math.duke.edu
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[2] K. Appa , Finite-Surface Spline, Journal of Aircraft, Vol. 26, No.5, 1989, pp. 495496.

[3] S. Badia , F. Nobile , and C. Vergara , Fluid-structure partitioned procedures based on robin transmission conditions, Journal of Computational Physics, Vol. 227, 2008, pp. 70277051.

[4] K. J. Bathe , C. Nitikitpaiboon and X. Wang , A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers &Structures, Vol. 56, 1995, pp. 225237.

[5] J. T. Beale and A. T. Layton , On the accuracy of finite difference methods for elliptic problems with interfaces, Communications in Applied Mathematics and Computational Sciences, Vol. 1, 2006, pp. 91119.

[6] J. T. Beale and A. T. Layton , A velocity decomposition approach for moving interfaces in viscous fluids, Journal of Computational Physics, Vol. 228, 2009, pp. 33583367.

[8] P. A. Berthelsen and O. M. Faltinsen , A local directional ghost cell approach for incompressible viscous flow problems with irregular boundaries, Journal of Computational Physics, Vol. 227, 2008, pp. 43544397.

[9] R. P. Beyer , A computational model of the cochlea using the immersed boundary methods, Journal of Computational Physics, Vol. 98, 1992, pp. 145162.

[13] P. Causin , J. F. Gerbeau and F. Nobile , Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Computer Methods in Applied Mechanics and Engineering, Vol. 194, 2005, pp. 45064527.

[14] J. R. Cebral and R Lohner , Conservative load projection and tracking for fluid-structure problems, AIAA Journal, Vol. 35, No.4, 1997, pp. 687691.

[18] R. Cortez and M. L. Minion , The blob projection method for immersed boundary problems, Journal of Computational Physics, Vol. 161, 2000, pp. 428453.

[19] J. Degroote , P. Bruggeman , R. Haelterman and J. Vierendeels , Stability of a coupling technique for partitioned solvers in FSI applications, Computers and Structures, Vol. 86, 2008, pp. 22242234.

[20] M. D. de Tullion , P. De Palma , G. Iaccarino , G. Pascazio , and M. Napolitano , An immersed boundary method for compressible flows using local grid refinement, Journal of Computational Physics, Vol. 225, 2007, pp. 20982117.

[21] R. Dillon , L. Fauci and D. Gaver III, A microscale model of bacterial swimming, chemotaxis, and substrate transport, Journal of Theoretical Biology, Vol. 177, 1995, pp. 325340.

[22] J. Dolbow , N. Moés and T. Belytschko , An extended finite element method for modeling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering, Vol. 190, 2001, pp. 68256846.

[23] E. H. Dowell and K. C. Hall , Modeling of fluid-structure interaction, Annual Review of Fluid Mechanics, Vol. 33, 2001, pp. 445490.

[24] E. A. Fadlun , R. Verzicco , P. Orlandi and J. Mohd-Yusof , Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, Journal of Computational Physics, Vol. 161, 2000, pp. 3560.

[26] L. Fauci and McDonald A. , Sperm mobility in the presence of boundaries, Bulletin of Mathematical Biology, Vol. 57, 1995, 679699.

[27] C. Farhat , K. G. van der Zee and P. Geuzaine , 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. 19732001.

[30] R. Glowinski , T.-W. Pan , T. I. Hesla , and D. D. Joseph , A distributed Lagrange multiplier/fictitious domain method for particulate flows, International Journal of Multiphase Flow, Vol. 25, 1999, pp. 755794.

[31] R. Glowinski , T.-W. Pan , T. I. Hesla , D. D. Joseph , and J. Periaux , 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. 241268.

[32] R. Glowinski , T.-W. Pan , T. I. Hesla , D. D. Joseph , and J. Periaux , 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. 363427.

[33] D. Goldstein , R. Handler and L. Sirovich , Modeling a no-slip flow boundary with an external force field, Journal of Computational Physics, Vol. 105, 1993, pp. 354366.

[35] B. E. Griffith and C. S. Peskin , 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. 75105.

[36] D. G. E. Grigoriadis , S. C. Kassinos and E. V. Votyakov , Immersed boundary method for the MHD flows of liquid metals, Journal of Computational Physics, Vol. 228, 2009, pp. 903920.

[38] R. D. Guy and D. A. Hartenstine , On the accuracy of direct forcing immersed boundary methods with projection methods, Journal of Computational Physics, Vol. 229, 2010, pp. 24792496.

[39] W. Haase , Unsteady Aerodynamics Including Fluid/Structure Interaction, Air and Space Europe, Vol. 3, 2001, pp. 8386.

[41] C. W. Hirt and B. D. Nichols , Volume of fluid (VOF) method for dynamics of free boundaries, Journal of Computational Physics, Vol. 39, 1981, pp. 201225.

[44] T. Y. Hou , J. S. Lowengrub , and M. J. Shelley , Removing the stiffness from interfacial flows with surface tension., Journal of Computational Physics, Vol. 114, 1994, pp. 312338.

[45] T. Y. Hou and Z. Shi , An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, Journal of Computational Physics, Vol. 227, 2008, pp. 89688991.

[46] T. Y. Hou and Z. Shi , Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations, Journal of Computational Physics, Vol. 227, 2008, pp. 91389169.

[47] M. S. Howe , Acoustics of Fluid-Structure Interactions, Cambridge University Press, 1998.

[48] W. X. Huang and H. J. Sung , An immersed boundary method for fluid-flexible structure interaction, Computer Methods in Applied Mechanics and Engineering, Vol. 198, 2009, pp. 26502661.

[49] B. Hubner , E. Walhorn and D. Dinkler , A monolithic approach to fluid-structure interaction using space-time finite elements, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 20872104.

[50] G. Iaccarino and R. Verzicco , Immersed boundary technique for turbulent flow simulations, Applied Mechanics Review, Vol. 56, 2003, pp. 331347.

[51] S. R. Idelsohn , E. Onate , Del F. Pin and N. Calvo , Fluid-structure interaction using the particle finite element method, Computer Methodsin Applied Mechanics and Engineering, Vol. 195, 2006, pp. 21002123.

[52] S. R. Idelsohn , J. Marti , A. Limache and E. Onate , 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. 17621776.

[53] B. Irons and R. C. Tuck , A Version of the Aitken accelerator for computer implementation, International Journal for Numerical Methods in Engineering, Vol. 1, 1969, pp. 275277.

[54] P. G. Jayathilake , B. C. Khoo and Z. Tan , Effect of membrane permeability on capsule substrate adhesion: Computation using immersed interface method, Chemical Engineering Science, Vol. 65, 2010, pp. 35673578.

[57] D. Kim and H. Choi , Immersed boundary method for flow around an arbitrarily moving body, Journal of Computational Physics, Vol. 212, 2006, pp. 662680.

[58] J. Kim , D. Kim and H. Choi , An immersed-boundary finite-volume method for simulations of flow in complex geometries, Journal of Computational Physics, Vol. 171, 2001, pp. 132150.

[59] Y. Kim and C. S. Peskin , Penalty immersed boundary method for an elastic boundary with mass, Physics of Fluids, Vol. 19, 053103, 2007, pp. 118.

[60] M. C. A. Kropinski , An efficient numerical method for studying interfacial motion in two-dimensional creeping flows, Journal of Computational Physics, Vol. 171, 2001, pp. 479508.

[61] P. Lallemand and L.-S. Luo , Lattice Boltzmann method for moving boundaries, Journal of Computational Physics, Vol. 184, 2003, pp. 406421.

[62] A. T. Layton , Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces, Computer and Fluids, Vol. 38, 2009, pp. 266272.

[64] D. V. Le , B. C. Khoo and K. M. Lim , An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 21192130.

[65] T. R. Lee , Y. S. Chang , J. B. Choi , D. W. Kim , W. K. Liu and Y. J. Kim , 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. 23052316.

[66] E. Lefranc¸ois and J.-P. Boufflet , An Introduction to Fluid-Structure Interaction: Application to the Piston Problem, SIAM Review, Vol. 52, 2010, pp. 747767.

[67] R. J. Leveque and Z. Li , Immersed interface method for Stokes flow with elastic boundaries or surface tension, SIAM Journal on Scientific Computing, Vol. 18, 1997, 709-735.

[68] L. Lee and LeVeque R. J. , An immersed interface method for the incompressible Navier-Stokes equations, SIAM Journal on Scientific Computing, Vol. 25, 2003, pp. 832856.

[70] Z. Li and K. Ito , The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, Society for Industrial and Applied Mathematic, 2006.

[72] Z. Li and M. C. Lai , The immersed interface method for the Navier-Stokes equations with singular forces, Journal of Computational Physics, Vol. 171, 2001, pp. 822842.

[73] Z. Li , M.-C. Lai , G. He and H. Zhao , An augmented method for free boundary problems with moving contact lines, Computers &Fluids, Vol. 39, 2010, pp. 10331040.

[74] W. K. Liu , D. W. Kim and S. Tang , Mathematical foundations of the immersed finite element method, Computational Mechanics, Vol. 39, 2006, pp. 211222.

[75] W. K. Liu , Y. Liu , D. Farrell , L. Zhang , X. Wang , Y. Fukui , N. Patankar , Y. Zhang , C. Bajaj , X. Chen and H. Hsu , Immersed finite element method and its applications to biological systems, Computer Methods in Applied Mechanics and Engineering, Vol. 195, 2006, pp. 17221749.

[76] K. Luo , Z. Wang and J. Fan , A modified immersed boundary method for simulation of fluid-particle interactions, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2007, pp. 3646.

[77] A. Mark and van B. G. M. Wachem , Derivation and validation of a novel implicit second-order accurate immersed boundary method, Journal of Computational Physics, Vol. 227, 2008, pp. 66606680.

[78] A. Mayo and C. S. Peskin , An implicit numerical method for fluid dynamics problems with immersed elastic boundaries, in Fluid Dynamics in Biology (Ed. A. Y. Cheer and C. P. von Dam ), pp. 261278, Providence, RI, 1993, AMS.

[80] C. Michler , S. J. Hulshoff , E. H. van Brummelen and R. de Borst , A monolithic approach to fluid-structure interaction, Computers &Fluids, Vol. 33, 2004, pp. 839848.

[81] R. Mittal and G. Iaccarino , Immersed boundary methods, Annual Review of Fluid Mechanics, Vol. 37, 2005, pp. 239261.

[82] R. Mittal , H. Dong , M Bozkurttas and F. M. Najjar , A versatile sharp interface immersed boundary method for incompressible flow with complex boundaries, Journal of Computational Physics, Vol. 227, 2008, pp. 48254852.

[83] N. Moés , J. Dolbow and T. Belytschko , A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, Vol. 46, 1999, pp. 131150.

[86] Y. Mori and C. S. Peskin , Implicit second order immersed boundary methods with boundary mass., Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 20492067.

[88] E. Newren , A. Fogelson , R. Guy , and M. Kirby , A comparison of implicit solvers for the immersed boundary equations, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 22902304.

[89] J. c. Newman III, P. A. Newman , A. C. Taylor III, and G. J.-W. Hou , Efficient non-linear static aeroelastic wing analysis, International Journal of Computers and Fluids, Vol. 28, January 1999, pp. 615628.

[90] J. Nocedal and S. J. Wright , Numerical Optimization, Springer, 1999.

[92] S. Osher and J. A. Sethian , Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, Vol. 79, 1988, pp. 1249.

[96] C. S. Peskin , Numerical analysis of blood flow in the heart, Journal of Computational Physics, Vol. 25, 1977, pp. 220252.

[97] C. S. Peskin , The immersed boundary method, Acta Numerica, Vol. 11, 2002, pp. 479517.

[98] C. S. Peskin and B. F. Printz , Improved volume conservation in the computation of flows with immersed elastic boundaries, Journal of Computational Physics, Vol. 105, 1993, pp. 3346.

[99] I. Ramiere , P. Angot and M. Belliard , A general ficitious domain method with immersed jumps and multilevel nested structured meshes, Journal of Computational Physics, Vol. 225, 2007, pp. 13471387.

[101] A. M. Roma , C. S. Peskin and M. J. Berger , An adaptive version of the immersed boundary method, Journal of Computational Physics, Vol. 153, 1999, pp. 509534.

[103] P. B. Ryzhakov , R. Rossi , S. R. Idelsohn and E. Oñate , A monolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, Vol. 46, 2010, pp. 883899.

[108] J. A. Samareh , Status and future of geometry modeling and grid generation for design and optimization, Journal of Aircraft, Vol. 36, No. I, 1999, pp. 97104.

[112] J. S. Sohn , Y.-H. Tseng , S. Li , A. Voigt , and J. S. Lowengrub , Dynamics of multicom-ponent vesicles in a viscous fluid, Journal of Computational Physics, Vol. 229, 2010, pp. 119144.

[114] J. M. Stockie , and S. I. Green , Simulating the motion of flexible pulp fibres using the immersed boundary method, Journal of Computational Physics, Vol. 147, 1998, pp. 147165.

[115] J. M. Stockie and B. R. Wetton , Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes, Journal of Computational Physics, Vol. 154, 1999, pp. 4164.

[116] C. H. Tai , K. M. Liew and Y. Zhao , Numerical simulation of 3D fluid-structure interaction flow using an immersed object method with overlapping grids, Computers and Structures, Vol. 85, 2007, pp. 749762.

[118] K. Taira and T. Colonius , The immersed boundary method: A project approach, Journal of Computational Physics, Vol. 225, 2007, pp. 21182137.

[119] Z. Tan , D. V. Le , K. M. Lim and B. C. Khoo , 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. 17981819.

[120] Z. Tan , K. M. Lim and B. C. Khoo , An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries, Journal of Computational Physics, Vol. 228, 2009, pp. 68556881.

[121] A.-K. Tornberg and B. Engquist , Numerical approximations of singular source terms in differential equations, Journal of Computational Physics, Vol. 200, 2004, pp. 462488.

[122] A.-K. Tornberg and M. J. Shelley , Simulating the dynamics and interactions of flexible fibers in Stokes flow, Journal of Computational Physics, Vol. 196, 2004, pp. 840.

[123] Y.-H. Tseng and J. H. Ferziger , A ghost-cell immersed boundary method for flow in complex geometry, Journal of Computational Physics, Vol. 192, 2003, pp. 593623.

[124] C. Tu and C. S. Peskin 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. 13611376.

[126] H. S. Udaykumar , R. Mittal and W. Shyy , Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids, Journal of Computational Physics, Vol. 153, 1999, pp. 534574.

[127] H. S. Udaykumar , R. Mittal , P. Rampunggoon , A. Khanna , A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, Journal of Computational Physics, Vol. 174, 2001, pp. 345380.

[128] H. S. Udaykumar , W. Shyy and M. M. Rao , 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. 691705.

[129] S. K. Veerapaneni , D. Gueyffier , D. Zorin , and G. Biros , 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. 23342353.

[130] J. Vierendeels , K. Dumont and P. R. Verdonck , A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics, Journal of Computational and Applied Mathematics, Vol. 215, 2008, pp. 602609.

[131] A. Wachs , 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. 183198.

[134] X. S. Wang , From immersed boundary method to immersed continuum method, International Journal for Multiscale Computational Engineering, Vol. 4, No. 1, 2006, pp. 127145.

[135] X. S. Wang , An iterative matrix-free method in implicit immersed boundary/continuum method, Computers and Structures, Vol. 85, 2007, pp. 739748.

[136] X. S. Wang , Immersed boundary/continuum methods, in Computational Modeling in Biomechanics, S. De et al. (Eds.), Springer, 2010, pp. 348.

[137] X. S. Wang and W. K. Liu , Extended immersed boundary method using FEM and RKPM, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 13051321.

[138] X. S. Wang , L. T. Zhang and W. K. Liu , On computational issues of immersed finite element methods, Journal of Computational Physics, Vol. 228, 2009, pp. 25352551.

[141] C. Wood , A. J. Gil , O. Hassan and J. Bonet , Partitioned block-gauss-seidel coupling for dynamic fluid-structure interaction, Computers and Structures, Vol. 88, 2010, pp. 13671382.

[142] S. Xu and Z. J. Wang , A 3D immersed interface method for fluid-solid interaction, Computer Methods in Applied Mechanics and Engineering, Vol. 197, 2008, pp. 20682086.

[143] J. Yang and E. Balaras , An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, Journal of Computational Physics, Vol. 215, 2006, pp. 1240.

[144] T. Ye , R. Mittal , H. S. Udaykumar and W. Shyy , An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, Journal of Computational Physics, Vol. 156, 1999, pp. 209240.

[145] Z. Yu , A DLM/FD method for fluid/flexible-body interactions, Journal of Computational Physics, Vol. 207, 2005, pp. 127.

[146] Z. Yu and X. Shao , A direct-forcing fictitious domain method for particulate flows, Journal of Computational Physics, Vol. 227, 2007, pp. 292314.

[147] L. T. Zhang , A. Gerstenberger , X. Wang and W. K. Liu , Immersed finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 193, 2004, pp. 20512067.

[148] L. T. Zhang and M. Gay , Immersed finite element method for fluid-structure interactions, Journal of Fluids and Structures, Vol. 23, No. 6, 2007, pp. 839857.

[149] L. T. Zhang , G. J. Wagner and W. K. Liu , Modeling and simulation of fluid structure interaction by meshfree and FEM, Communications in Numerical Methods in Engineering, Vol. 19, 2003, pp. 615621.

[150] W. Zhang , Y. Jiang and Z. Ye , Two better loosely coupled solution algorithms of CFD based aeroelastic simulation, Engineering Applications of Computational Fluid Mechanics, Vol. 1, No. 4, 2007, pp. 253262.

[151] H. Zhao , J. B. Freund and R. D. Moser , A fixed-mesh method for incompressible flow-structure systems with finite solid deformation, Journal of Computational Physics, Vol. 227, 2008, pp. 31143140.

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