Computational Mechanics

, Volume 40, Issue 1, pp 167–183 | Cite as

Computation of free-surface flows and fluid–object interactions with the CIP method based on adaptive meshless soroban grids

  • Kenji Takizawa
  • Takashi Yabe
  • Yumiko Tsugawa
  • Tayfun E. Tezduyar
  • Hiroki Mizoe
Original Paper


The CIP Method [J comput phys 61:261–268 1985; J comput phys 70:355–372, 1987; Comput phys commun 66:219–232 1991; J comput phys 169:556–593, 2001] and adaptive Soroban grid [J comput phys 194:57–77, 2004] are combined for computation of three- dimensional fluid–object and fluid–structure interactions, while maintaining high-order accuracy. For the robust computation of free-surface and multi-fluid flows, we adopt the CCUP method [Phys Soc Japan J 60:2105–2108 1991]. In most of the earlier computations, the CCUP method was used with a staggered-grid approach. Here, because of the meshless nature of the Soroban grid, we use the CCUP method with a collocated-grid approach. We propose an algorithm that is stable, robust and accurate even with such collocated grids. By adopting the CIP interpolation, the accuracy is largely enhanced compared to linear interpolation. Although this grid system is unstructured, it still has a very simple data structure.


Grid Point Structure Interaction Spatial Derivative Cartesian Grid Grid Generation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Takewaki H, Nishiguchi A, Yabe T (1985) The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations. J Comput Phys 61:261–268zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Takewaki H, Yabe T (1987) Cubic-interpolated pseudo particle (CIP) method – Application to nonlinear or multi-dimensional problems. J Comput Phys 70:355–372zbMATHCrossRefGoogle Scholar
  3. 3.
    Yabe T, Aoki T (1991) A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver. Comput Phys Commun 66:219–232zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Yabe T, Xiao F, Utsumi T (2001) Constrained interpolation profile method for multiphase analysis. J Comput Phys 169:556–593zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Yabe T, Mizoe H, Takizawa K, Moriki H, Im H, Ogata Y (2004) Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme. J Comput Phys 194:57–77zbMATHCrossRefGoogle Scholar
  6. 6.
    Yabe T, Wang PY (1991) Unified numerical procedure for compressible and incompressible fluid. Phys Soc Jpn J 60:2105–2108CrossRefGoogle Scholar
  7. 7.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – The deforming-spatial-domain/space–time procedure: I The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – The deforming-spatial-domain/space–time procedure: II Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Johnson AA, Tezduyar TE (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Johnson AA, Tezduyar TE (1997) 3D simulation of fluid-particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng 145:301–321zbMATHCrossRefGoogle Scholar
  11. 11.
    Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows – Fluid-structure interactions. Int J Numerical Methods Fluids 21:933–953zbMATHCrossRefGoogle Scholar
  12. 12.
    Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D Computation. Comput Methods Appl Mech Eng 190:373–386zbMATHCrossRefGoogle Scholar
  13. 13.
    Wall W (1999) Fluid–Structure Interaction with Stabilized Finite Elements. Ph.D. thesis, University of StuttgartGoogle Scholar
  14. 14.
    Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems.Comput Methods Appl Mech Eng 193:1–23zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hubner B, Walhorn E, Dinkler D (2004) A monolithic approach to fluid–structure interaction using space–time finite elements. Comput Methods Appl Mech Eng 193:2087–2104CrossRefGoogle Scholar
  16. 16.
    Dettmer W (2004) Finite element modeling of fluid flow with moving free surfaces and interfaces including fluid–solid interaction. Ph.D. thesis, University of Wales SwanseaGoogle Scholar
  17. 17.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130zbMATHGoogle Scholar
  18. 18.
    Berger MJ, Oliger J (1984) Adaptive mesh refinement for hyperbolic partial differential equations. J Comput Phys 53:484–512zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kirkpatrick MP, Armfield SW, Kent JH (2003) A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid. J Comput Phys 184:1–36zbMATHCrossRefGoogle Scholar
  20. 20.
    Unverdi SO, Tryggvasson GA (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100:25–37zbMATHCrossRefGoogle Scholar
  21. 21.
    Enright D, Fedkiw R, Ferziger J, Mitchell I (2002) A hybrid particle level set method for improved interface capturing. J Comput Phys 183:83–116zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Harlow FH, Amsden AA (1968) Numerical calculation of almost incompressible flow. J Comput Phys 3:80–93zbMATHCrossRefGoogle Scholar
  23. 23.
    Yoon SY, Yabe T (1999) The unified simulation for incompressible and compressible flow by the predictor-corrector scheme based on the CIP method. Comput Phys Commun 119:149–158zbMATHCrossRefGoogle Scholar
  24. 24.
    Aoki T (1995) Multi-dimensional advection of CIP (cubic-interpolate propagation) scheme. CFD J 4:279–291Google Scholar
  25. 25.
    Staniforth A, Côté J (1991) Semi-Lagrangian integration scheme for atmospheric models - A review. Mon Weather Rev 119:2206–2223CrossRefGoogle Scholar
  26. 26.
    Ogata Y, Yabe T (1999) Shock capturing with improved numerical viscosity in primitive Euler representation. Comput Phys Commun 119:1799–193Google Scholar
  27. 27.
    Tezduyar TE, Liou J, Ganjo DK (1990) Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations. Comput Struct 35:445–472zbMATHCrossRefGoogle Scholar
  28. 28.
    van der Vorst HA (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non symmetric linear systems. SIAM J Sci Stat Comput 13:631–644zbMATHCrossRefGoogle Scholar
  29. 29.
    Lee J, Zhang J, Lu C (2003) Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems. J Comput Phys 185:158–175zbMATHCrossRefGoogle Scholar
  30. 30.
    Show E, Saad Y (1997) Experimental study of ILU preconditioners for indefinite matrices. J Comput Appl Math 86:387–414CrossRefMathSciNetGoogle Scholar
  31. 31.
    Yabe T, Xiao F (1993) Description of complex and sharp interface during shock wave interaction with liquid drop. Phys Soc Jpn J 62:2537–2540CrossRefGoogle Scholar
  32. 32.
    Takizawa K, Yabe T, Chino M, Kawai T, Wataji K, Hoshino H, Watanabe T (2005) Simulation and experiment on swimming fish and skimmer by CIP method. Comput Struct 83:397–408CrossRefGoogle Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Takashi Yabe
    • 2
  • Yumiko Tsugawa
    • 2
  • Tayfun E. Tezduyar
    • 3
  • Hiroki Mizoe
    • 4
  1. 1.National Maritime Research InstituteTokyoJapan
  2. 2.Tokyo Institute of TechnologyTokyoJapan
  3. 3.Mechanical Engineering, Rice UniversityHoustonUSA
  4. 4.Tohoku Electric Power Company, IncSendaiJapan

Personalised recommendations