Journal of Hydrodynamics

, Volume 30, Issue 5, pp 890–897 | Cite as

A radial basis function for reconstructing complex immersed boundaries in ghost cell method

  • Jian-jian Xin (辛建建)
  • Ting-qiu Li (李廷秋)Email author
  • Fu-long Shi (石伏龙)


It is important to track and reconstruct the complex immersed boundaries for simulating fluid structure interaction problems in an immersed boundary method (IBM). In this paper, a polynomial radial basis function (PRBF) method is introduced to the ghost cell immersed boundary method for tracking and reconstructing the complex moving boundaries. The body surfaces are fitted with a finite set of sampling points by the PRBF, which is flexible and accurate. The complex or multiple boundaries could be easily represented. A simple treatment is used for identifying the position information about the interfaces on the background grid. Our solver and interface reconstruction method are validated by the case of a cylinder oscillating in the fluid. The accuracy of the present PRBF method is comparable to the analytic function method. In ta flow around an airfoil, the capacity of the proposed method for complex geometries is well demonstrated.

Key words

Immersed boundary method (IBM) polynomial radial basis function ghost cell method interface reconstruction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Mittal R., Iaccarino G. Immersed boundary methods [J]. Annual Review Fluid Mechanics, 2005, 37: 239–261.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Yang J. Sharp interface direct forcing immersed boundary methods: A summary of some algorithms and applications [J]. Journal of Hydrodynamics, 2016, 28(5): 713–730.CrossRefGoogle Scholar
  3. [3]
    Yang F. C., Chen X. P. Numerical simulation of twodimensional viscous flows using combined finite element-immersed boundary method [J]. Journal of Hydrodynamics, 2015, 27(5): 658–667.CrossRefGoogle Scholar
  4. [4]
    Luo K., Mao C., Zhuang Z. et al. A ghost-cell immersed boundary method for the simulations of heat transfer in compressible flows under different boundary conditions Part-II: Complex geometries [J]. International Journal of Heat and Mass Transfer, 2017, 104(1): 98–111.CrossRefGoogle Scholar
  5. [5]
    Dechristé G., Mieussens L. A Cartesian cut cell method for rarefied flow simulations around moving obstacles [J]. Journal of Computational Physics, 2016, 314(1): 465–488.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Tang C., Lu X. Y. Self-propulsion of a three-dimensional flapping flexible plate [J]. Journal of Hydrodynamics, 2016, 28(1): 1–9.CrossRefGoogle Scholar
  7. [7]
    Wang K., Grétarsson J., Main A. et al. Computational algorithms for tracking dynamic fluid-structure interfaces in embedded boundary methods [J]. International Journal for Numerical Methods in Fluids, 2012, 70(4): 515–535.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Boukharfane R., Ribeiro F. H. E., Bouali Z. et al. A combined ghost-point-forcing / direct-forcing immersed boundary method (IBM) for compressible flow simulations [J]. Computers and Fluids, 2018, 162(1): 91–112.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Wang W. A non-body conformal grid method for simulations of laminar and turbulent flows with a compressible large eddy simulation solver [D]. Doctoral Thesis, Iowa, USA: Iowa State University, 2009.CrossRefGoogle Scholar
  10. [10]
    Borazjani I., Liang G., Sotiropoulos F. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies [J]. Journal of Computational Physics, 2008, 227(16): 7587–7620.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Lin P. A fixed-grid model for simulation of a moving body in free surface flows [J]. Computers and Fluids, 2007, 36(3): 549–561.CrossRefzbMATHGoogle Scholar
  12. [12]
    Schneiders L., Hartmann D., Meinke M. et al. An accurate moving boundary formulation in cut-cell methods [J]. Journal of Computational Physics, 2013, 235(4): 786–809.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Günther C., Meinke M., Schröder W. A flexible level-set approach for tracking multiple interacting interfaces in embedded boundary methods [J]. Computers and Fluids, 2014, 102(10): 182–202.CrossRefGoogle Scholar
  14. [14]
    Raees F., Heul D. R., Vuik C. A mass-conserving level-set method for simulation of multiphase flow in geometrically complicated domains [J]. International Journal for Numerical Methods in Fluids, 2016, 81(7): 399–425.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Xin J. J., Shi F. L., Qiu J. et al. Numerical simulation of complex immersed boundary flow by a radial basis function ghost cell method [J]. Acta Physica Sinica, 2017, 66(4): 044704.Google Scholar
  16. [16]
    Ye J., Li T., Chang X. et al. Impact of landslide- generated waves on the motion of a complex multibody in the restricted area by a two-phase solver [C]. The Twentythird International Offshore and Polar Engineering Conference, Alaska, USA, 2013, 650–656.Google Scholar
  17. [17]
    Clavero C., Jorge J. C. A fractional step method for 2D parabolic convection-diffusion singularly perturbed problems: uniform convergence and order reduction [J]. Numerical Algorithms, 2016, 75(3): 1–18.MathSciNetGoogle Scholar
  18. [18]
    Shin B. R. Numerical simulation for the turbulent flow through hydrodynamic component using finite volume method [C]. European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, Spain, 2000.Google Scholar
  19. [19]
    Pan D., Shen T. T. Computation of incompressible flows with immersed bodies by a simple ghost cell method [J]. International Journal for Numerical Methods in Fluids, 2009, 60(12): 1378–1401.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Guilmineau E., Queutey P. A numerical simulation of vortex shedding from an oscillating circular cylinder [J]. Journal of Fluids and Structures, 2002, 16(6): 773–794.CrossRefGoogle Scholar
  21. [21]
    Imamura T., Suzuki K., Nakamura T. et al. Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method [J]. Journal of Computational Physics, 2005, 202(2): 645–663.CrossRefzbMATHGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Jian-jian Xin (辛建建)
    • 1
  • Ting-qiu Li (李廷秋)
    • 1
    Email author
  • Fu-long Shi (石伏龙)
    • 1
  1. 1.Key Laboratory of High Performance Ship Technology of Ministry of Education, School of TransportationWuhan University of TechnologyWuhanChina

Personalised recommendations