Journal of Hydrodynamics

, Volume 23, Issue 4, pp 476–482 | Cite as

Numerical Method for Multi-Body Fluid Interaction Based on Immersed Boundary Method

  • Ping-jian MingEmail author
  • Wen-ping Zhang


A Cartesian grid based on Immersed Boundary Method (IBM), proposed by the present authors, is extended to unstructured grids. The advantages of IBM and Body Fitted Grid (BFG) are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain. There are many methods to generate the BFG, among which the unstructured grid method is the most popular. The concept of Volume Of Solid (VOS) is used to deal with the multi rigid body and fluid interaction. Each body surface is represented by a set of points which can be traced in an anti-clockwise order with the solid area on the left side of surface. An efficient Lagrange point tracking algorithm on the fixed grid is applied to search the moving boundary grid points. This method is verified by low Reynolds number flows in the range from Re = 100 to 1 000 in the cavity with a moving lid. The results are in a good agreement with experimental data in literature. Finally, the flow past two moving cylinders is simulated to test the capability of the method.

Key words

fluid-structure interaction Immersed Boundary Method (IBM) Volume Of Solid (VOS) unstructured grids 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    FARAHAT C., GEUZAINE P. and GRANDMONT C. The discrete geometric conservation law and nonlinear stability of ALE schemes for solution of flow problems on moving grids[J]. Journal of Computational Physics, 2001, 174(2): 669–694.MathSciNetCrossRefGoogle Scholar
  2. [2]
    WANG Z. J., PARTHASARATHY V. A fully automated Chimera methodology for multiple moving body problems[J]. International Journal for Numerical Methods in Fluids, 2000, 33(7): 919–938.CrossRefGoogle Scholar
  3. [3]
    CHEN H. C., LIU T. Time domain simulation of large amplitude ship roll motions by a Chimera RANS method[J]. International Journal of Offshore and Polar Engineering, 2002, 12(3): 206–212.Google Scholar
  4. [4]
    GARCIA J., ONATE E. An unstructured finite element solver for ship hydrodynamics problems[J]. Journal of Applied Mechanics, 2003, 70(1): 18–27.CrossRefGoogle Scholar
  5. [5]
    PESKIN C. S. Flow patterns around heart valves: A numerical method[J]. Journal of Computational Physics, 1972, 10(2): 252–271.MathSciNetCrossRefGoogle Scholar
  6. [6]
    DUTSCH H., DURST F. and BECKER S. Low Reynolds number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers[J]. Journal of Fluid Mechanics, 1998, 360: 249–271.CrossRefGoogle Scholar
  7. [7]
    MITTAL R., IACCARINO G. Immersed boundary methods[J]. Annual Review Fluid Mechanics, 2005, 37: 239–61.Google Scholar
  8. [8]
    GHIAS R., MITTAL R. and DONG H. A sharp interface immersed boundary method for compressible viscous flows[J]. Journal of Computational Physics, 2007, 225(1): 528–553.MathSciNetCrossRefGoogle Scholar
  9. [9]
    ROMAN F., NAPOLI E. and MILICI B. et al. An improved immersed boundary method for curvilinear grids[J]. Computers and Fluids, 2009, 38(8): 1510–1527.CrossRefGoogle Scholar
  10. [10]
    UDAYKUMAR H. S., MITTAL R. and RAMPUNGGOON P. et al. A sharp interface cartesian grid method for simulating flows with complex moving boundaries[J]. Journal of Computational Physics, 2001, 174(1): 345–380.CrossRefGoogle Scholar
  11. [11]
    MING Ping-jian, ZHANG Wen-ping. Numerical simulation of low Reynolds number fluid-structure interaction with immersed boundary method[J]. Chinese Journal of Aeronautics, 2009, 22(5): 480–485.CrossRefGoogle Scholar
  12. [12]
    PAN D. An immersed boundary method for incompressible flows using volume of body function[J]. International Journal for Numerical Methods in Fluids, 2006, 50(6): 733–750.MathSciNetCrossRefGoogle Scholar
  13. [13]
    NG K. C. A collocated finite volume embedding method for simulation of flow past stationary and moving body[J]. Computers and Fluids, 2009, 38(2): 347–357.CrossRefGoogle Scholar
  14. [14]
    MING P. J., SUN Y. Z. and DUAN W. Y. et al. Unstructured grid immersed boundary method for numerical simulation of fluid structure interaction[J]. Journal of Marine Science and Application, 2010, 9(2): 181–186.CrossRefGoogle Scholar
  15. [15]
    LIU Yong-feng, MING Ping-jian and ZHANG Wenping et al. An efficient Lagrange point tracking algorithm for fixed grids[J]. Chinese Journal of Computational Physics, 2010, 27(4): 527–532(in Chinese).Google Scholar
  16. [16]
    MING Ping-jian, ZHANG Wen-ping and LU Xi-qun et al. Numerical simulation of fluid structure interaction based on combination of immersed boundary method and unstructured grids[J]. Chinese Journal of Hydrodynamics, 2010, 25(3): 323–331(in Chinese).Google Scholar
  17. [17]
    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.MathSciNetCrossRefGoogle Scholar
  18. [18]
    CALHOUN D. A Cartesian grid method for solving the two-dimensional stream function-vorticity equations in irregular region[J]. Journal of Computational Physics, 2002, 176(2): 231–27.MathSciNetCrossRefGoogle Scholar
  19. [19]
    RUSSELL D., WANG Z. J. A Cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow[J]. Journal of Computational Physics, 2003, 191(1): 177–205.MathSciNetCrossRefGoogle Scholar
  20. [20]
    JUNG-Il C., ROSHAN C. O. and JACK R. E. et al. An immersed boundary method for complex incompressible flows[J]. Journal of Computational Physics, 2007, 224(2): 757–784.MathSciNetCrossRefGoogle Scholar
  21. [21]
    SCHREIBER R., KELLER H. B. Driven cavity flows by efficient numerical techniques[J]. Journal of Computational Physics, 1983, 49(2): 310–333.CrossRefGoogle Scholar
  22. [22]
    JUN Z. Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes[J]. Computers and Mathematics with Applications, 2003, 45(1-3): 43–52.Google Scholar
  23. [23]
    GHIA U., GHIA K. N. and SHIN C. T. High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. Journal of Computational Physics, 1982, 48(3): 387–411.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2011

Authors and Affiliations

  1. 1.School of Power and Energy EngineeringHarbin Engineering UniversityHarbinChina

Personalised recommendations