Journal of Hydrodynamics

, Volume 28, Issue 5, pp 713–730 | Cite as

Sharp interface direct forcing immersed boundary methods: A summary of some algorithms and applications

  • Yang JianmingEmail author
Review article


Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.


immersed boundary methods direct forcing sharp interface method strong coupling schemes fluid-structure interactions Cartesian grid methods 


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  1. [1]
    LEONARD A. Computing three-dimensional incompressible flows with vortex elements[J]. Annual Review of Fluid Mechanics, 1985, 17(1): 523–559.MathSciNetCrossRefGoogle Scholar
  2. [2]
    MONAGHAN J. Smoothed particle hydrodynamics and its diverse applications[J]. Annual Review of Fluid Mechanics, 2012, 44: 323–346.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    TUCKER P., PAN Z. A cartesian cut cell method for incompressible viscous flow[J]. Applied Mathematical Modelling, 2000, 24(8): 591–606.zbMATHCrossRefGoogle Scholar
  4. [4]
    INGRAM D. M., CAUSON D. M. and MINGHAM C. G. Developments in cartesian cut cell methods[J]. Mathematics and Computers in Simulation, 2003, 61(3): 561–572.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    PESKIN C. S. Flow patterns around heart valves: A numerical method[J]. Journal of Computational Physics, 1972, 10(2): 252–271.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    PESKIN C. S. Numerical analysis of blood flow in the heart[J]. Journal of Computational Physics, 1977, 25(3): 220–252.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    PESKIN C. S. The immersed boundary method[J]. Acta Numerica, 2002, 11: 479–517.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    GOLDSTEIN D., HANDLER R. and SIROVICH L. Modeling a no-slip flow boundary with an external force field[J]. Journal of Computational Physics, 1993, 105(2): 354–366.zbMATHCrossRefGoogle Scholar
  9. [9]
    SAIKI E. M., BIRINGEN S. Numerical simulation of a cylinder in uniform flow: Application of a virtual boundary method[J]. Journal of Computational Physics, 1996, 123(2): 450–465.zbMATHCrossRefGoogle Scholar
  10. [10]
    MOHD-YUSOF J. Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries[R]. Stanford, CA, USA: Annual Research Briefs, Center for Turbulence Research. Stanford University, 1997, 317–327.Google Scholar
  11. [11]
    FADLUN E. A., VERZICCO R. and ORLANDI P. et al. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics, 2000, 161(1): 35–60.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    KIM J., KIM D. and CHOI H. An immersed-boundary finite-volume method for simulations of flow in complex geometries[J]. Journal of Computational Physics, 2001, 171(1): 132–150.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    TSENG Y. H., FERZIGER J. H. A ghost-cell immersed boundary method for flow in complex geometry[J]. Journal of Computational Physics, 2003, 192(2): 593–623.MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    BALARAS E. Modeling complex boundaries using an external force field on fixed cartesian grids in large-eddy simulations[J]. Computers and Fluids, 2004, 33(3): 375–404.zbMATHCrossRefGoogle Scholar
  15. [15]
    UHLMANN M. An immersed boundary method with direct forcing for the simulation of particulate flows[J]. Journal of Computational Physics, 2005, 209(2): 448–476.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    FENG Z. G., MICHAELIDES E. E. Proteus: A direct forcing method in the simulations of particulate flows[J]. Journal of Computational Physics, 2005, 202(1): 20–51.zbMATHCrossRefGoogle Scholar
  17. [17]
    ZHANG N., ZHENG Z. An improved direct-forcing immersed-boundary method for finite difference applications[J]. Journal of Computational Physics, 2007, 221(1): 250–268.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    VANELLA M., BALARAS E. A moving-least-squares reconstruction for embedded-boundary formulations[J]. Journal of Computational Physics, 2009, 228(18): 6617–6628.zbMATHCrossRefGoogle Scholar
  19. [19]
    YANG X., ZHANG X. and LI Z. et al. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations[J]. Journal of Computational Physics, 2009, 228(20): 7821–7836.MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    PINELLI A., NAQAVI I. and PIOMELLI U. et al. Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers[J]. Journal of Computational Physics, 2010, 229(24): 9073–9091.MathSciNetzbMATHCrossRefGoogle Scholar
  21. [21]
    KEMPE T., FRÖHLICH J. An improved immersed boundary method with direct forcing for the simulation of particle laden flows[J]. Journal of Computational Physics, 2012, 231(9): 3663–3684.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    YANG J., BALARAS E. An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries[J]. Journal of Computational Physics, 2006, 215(1): 12–40.MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    BALARAS E., YANG J. Nonboundary conforming methods for large-eddy simulations of biological flows[J]. Journal of Fluids Engineering, 2005, 127(5): 851–857.CrossRefGoogle Scholar
  24. [24]
    YANG J., PREIDIKMAN S. and BALARAS E. A strongly coupled, embedded-boundary method for fluid-structure interactions of elastically mounted rigid bodies[J]. Journal of Fluids and Structures, 2008, 24(2): 167–182.CrossRefGoogle Scholar
  25. [25]
    YANG J., STERN F. A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions[J]. Journal of Computational Physics, 2012, 231(15): 5029–5061.MathSciNetzbMATHCrossRefGoogle Scholar
  26. [26]
    YANG J., STERN F. Robust and efficient setup procedure for complex triangulations in immersed boundary simulations[J]. Journal of Fluids Engineering, 2014, 135(10): 101107.CrossRefGoogle Scholar
  27. [27]
    YANG J., STERN F. A non-iterative direct forcing immersed boundary method for strongly-coupled fluid-solid interactions[J]. Journal of Computational Physics, 2015, 295: 779–804.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    YANG J., STERN F. Sharp interface immersed-boundary/level-set method for wave-body interactions[J]. Journal of Computational Physics, 2009, 228(17): 6590–6616.MathSciNetzbMATHCrossRefGoogle Scholar
  29. [29]
    YANG J., STERN F. Efficient simulation of fully coupled wave-body interactions using a sharp interface immersed-boundary/level-set method[C]. Proceedings of ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting. Montreal, Canada, 2010.Google Scholar
  30. [30]
    YANG J., STERN F. A sharp interface direct forcing immersed boundary approach for fully resolved simulations of particulate flows[J]. Journal of Fluids Engineering, 2013, 136(4): 040904.CrossRefGoogle Scholar
  31. [31]
    BEDDHU M., TAYLOR L. K. and WHITFIELD D. L. Strong conservative form of the incompressible Navier-Stokes equations in a rotating frame with a solution procedure[J]. Journal of Computational Physics, 1996, 128(2): 427–437.zbMATHCrossRefGoogle Scholar
  32. [32]
    KIM D., CHOI H. Immersed boundary method for flow around an arbitrarily moving body[J]. Journal of Computational Physics, 2006, 212(2): 662–680.MathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    LEONARD B. P. A stable and accurate convective modelling procedure based on quadratic upstream interpolation[J]. Computer Methods in Applied Mechanics and Engineering, 1979, 19(1): 59–98.MathSciNetzbMATHCrossRefGoogle Scholar
  34. [34]
    JIANG G.-S., SHU C.-W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202–228.MathSciNetzbMATHCrossRefGoogle Scholar
  35. [35]
    BEAM R. M., WARMING R. F. An implicit finite-difference algorithm for hyperbolic systems in conservationlaw form[J]. Journal of Computational Physics, 1976, 22(1): 87–110.MathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    MATTOR N., WILLIAMS T. J. and HEWETT D. W. Algorithm for solving tridiagonal matrix problems in parallel[J]. Parallel Computing, 1995, 21(11): 1769–1782.MathSciNetCrossRefGoogle Scholar
  37. [37]
    CHOI H., MOIN P. Effects of the computational time step on numerical solutions of turbulent flow[J]. Journal of Computational Physics, 1994, 113(1): 1–4.zbMATHCrossRefGoogle Scholar
  38. [38]
    BROWN P. N., FALGOUT R. D. and JONES J. E. et al. Semicoars ening multigrid on distributed memory machines[J]. SIAM Journal on Scientific Computing, 2000, 21(5): 1823–1834.MathSciNetzbMATHCrossRefGoogle Scholar
  39. [39]
    SWARZTRAUBER P. N. A direct method for the discrete solution of separable elliptic equations[J]. SIAM Journal on Numerical Analysis, 1974, 11(6): 1136–1150.MathSciNetzbMATHCrossRefGoogle Scholar
  40. [40]
    POPINET S. The GNU triangulated surface library[OL]., [Online, accessed 1-January-2012], 2011.Google Scholar
  41. [41]
    O’ROURKE J. Computational geometry in C[M]. 2nd Edition, New York, USA: Cambridge University Press, 1998.zbMATHGoogle Scholar
  42. [42]
    IACCARINO G., VERZICCO R. Immersed boundary technique for turbulent flow simulations[J]. Applied Mechanics Reviews, 2003, 56(3): 331–347.CrossRefGoogle Scholar
  43. [43]
    ERICSON C. Real-time collision detection[M]. San Francisco, USA: Morgan Kaufmann Publishers, 2005.Google Scholar
  44. [44]
    MORDANT N., PINTON J. F. Velocity measurement of a settling sphere[J]. European Physical Journal B - Condensed Matter and Complex Systems, 2000, 18(2): 343–352.CrossRefGoogle Scholar
  45. [45]
    GLOWINSKI R., PAN T. and HESLA T. et al. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow[J]. Journal of Computational Physics, 2001, 169(2): 363–426.MathSciNetzbMATHCrossRefGoogle Scholar
  46. [46]
    ANDERSEN A., PESAVENTO U. and WANG Z. J. Unsteady aerodynamics of fluttering and tumbling plates[J]. Journal of Fluid Mechanics, 2005, 541: 65–90.MathSciNetzbMATHCrossRefGoogle Scholar
  47. [47]
    STERN Frederick, WANG Zhao-yuan and YANG Jianming et al. Recent progress in CFD for naval architecture and ocean engineering[J]. Journal of Hydrodynamics, 2015, 27(1): 1–23.CrossRefGoogle Scholar
  48. [48]
    LIU P. L. F., WU T. R. and RAICHLEN F. et al. Runup and rundown generated by three-dimensional sliding masses[J]. Journal of Fluid Mechanics, 2005, 536: 107–144.zbMATHCrossRefGoogle Scholar
  49. [49]
    YANG J., BHUSHAN S. and SUH J., et al. Large-eddy simulation of ship flows with wall-layer models on Cartesian grids[C]. Proceedings of the 27th Symposium on Naval Hydrodynamics, Seoul, Korea, 2008.Google Scholar
  50. [50]
    BHUSHAN S., CARRICA P. M. and YANG J. et al. Scalability studies and large grid computations for surface combatant using CFD Ship-Iowa[J]. International Journal of High Performance Computing Applications (in Press).Google Scholar
  51. [51]
    PAIK K. J., CARRICA P. M. and LEE D. et al. Strongly coupled fluid-structure interaction method for structural loads on surface ships[J]. Ocean Engineering, 2009, 36(17–18): 1346–1357.CrossRefGoogle Scholar
  52. [52]
    YU Zhao-sheng, SHAO Xue-ming. A three-dimensional fictitious domain method for the simulation of fluid-structure interactions[J]. Journal of Hydrodynamics, 2010, 22(5Suppl.): 178–183.CrossRefGoogle Scholar
  53. [53]
    LIAO K., HU C. A coupled fdm-fem method for free surface flow interaction with thin elastic plate[J]. Journal of Marine Science and Technology, 2013, 18(1): 1–11.CrossRefGoogle Scholar
  54. [54]
    SHIN Sangmook, BAE Sung Yong. Simulation of water entry of an elastic wedge using the FDS scheme and HCIB method[J]. Journal of Hydrodynamics, 2013, 25(3): 450–458.CrossRefGoogle Scholar
  55. [55]
    TANG Chao, LU Xi-yun. Self-propulsion of a three-dimensional flapping flexible plate[J]. Journal of Hydrodynamics, 2016, 28(1): 1–9.CrossRefGoogle Scholar
  56. [56]
    LUO Xian-wu, JI Bin and TSUJIMOTO Yoshinobu. A review of cavitation in hydraulic machinery[J]. Journal of Hydrodynamics, 2016, 28(3): 335–358.CrossRefGoogle Scholar
  57. [57]
    BALARAS E., SCHROEDER S. and POSA A. Largeeddy simulations of submarine propellers[J]. Journal of Ship Research, 2015, 59(4): 227–237.CrossRefGoogle Scholar
  58. [58]
    MICHAEL T., YANG J. and STERN F. Sharp interface cavitation modeling using volume-of-fluid and level set methods[C]. Proceedings of the ASME 2013 Fluids Engineering Summer Meeting. Incline Village, Nevada, USA, 2013, FEDSM2013-16479.Google Scholar

Copyright information

© China Ship Scientific Research Center 2016

Authors and Affiliations

  1. 1.Fidesi Solutions LLCIowa CityUSA

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