Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1163–1172 | Cite as

Combined adaptive meshing technique and characteristic-based split algorithm for viscous incompressible flow analysis

  • Suthee Traivivatana
  • Parinya Boonmarlert
  • Patcharee Theeraek
  • Sutthisak Phongthanapanich
  • Pramote DechaumphaiEmail author


A combined characteristic-based split algorithm and an adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. The method uses the three-node triangular element with equal-order interpolation functions for all variables of the velocity components and pressure. The main advantage of the combined method is that it improves the solution accuracy by coupling an error estimation procedure to an adaptive meshing technique that generates small elements in regions with a large change in solution gradients, and at the same time, larger elements in the other regions. The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder, for their transient and steady-state flow behaviors.

Key words

adaptive mesh characteristic-based split finite element method incompressible flow 

Chinese Library Classification


2000 Mathematics Subject Classification

76D 76M25 


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  1. [1]
    Yamada Y, Ito K, Yokouchi Y, Tamano T, Ohtsubo T. Finite element analysis of steady fluid and metal flow[J]. Finite Elements in Fluids: Viscous Flow and Hydrodynamics, 1974, 1:73–94.Google Scholar
  2. [2]
    Kawahara M. Steady and unsteady finite element analysis of incompressible viscous fluid[J]. Finite Elements in Fluids, 1974, 3:23–54.Google Scholar
  3. [3]
    Kawahara M, Yoshimura N, Nakagawa K, Ohsaka H. Steady and unsteady finite element analysis of incompressible viscous fluid[J]. International Journal for Numerical Methods in Engineering, 1976, 10:437–456.zbMATHCrossRefGoogle Scholar
  4. [4]
    Christie I, Griffiths D F, Mitchell A R, Zienkiewicz O C. Finite element methods for second order differential equations with significant first derivative[J]. International Journal for Numerical Methods in Engineering, 1976, 10:1389–1396.zbMATHCrossRefGoogle Scholar
  5. [5]
    Heinrich J C, Huyakorn P S, Zienkiewicz O C, Mitchell A R. An upwind finite element scheme for two-dimensional convective transport equation[J]. International Journal for Numerical Methods in Engineering, 1977, 11:131–143.zbMATHCrossRefGoogle Scholar
  6. [6]
    Brooks A N, Heghes T J R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering, 1982, 32:199–259.zbMATHCrossRefGoogle Scholar
  7. [7]
    Wansophark N, Dechaumphai P. Enhancement of streamline upwinding finite element solutions by adaptive meshing technique[J]. JSME International Journal, Series B, Fluids and Thermal Engineering, 2002, 45:770–779.CrossRefGoogle Scholar
  8. [8]
    Zienkiewicz O C, Codina R. A General algorithm for compressible and incompressible flow-part I: the split, characteristic-based scheme[J]. International Journal for Numerical Methods in Fluids, 1995, 20:869–885.zbMATHCrossRefGoogle Scholar
  9. [9]
    Dechaumphai P, Phongthanapanich S. Adaptive Delaunay triangulation with multidimensional dissipation scheme for high-speed compressible flow analysis[J]. Applied Mathematics and Mechanics(English Edition), 2005, 26:1341–1356.Google Scholar
  10. [10]
    Phongthanapanich S, Dechaumphai P. Evaluation of combined Delaunay triangulation and remeshing for finite element analysis of conductive heat transfer[J]. Transactions of the Canadian Society for Mechanical Engineering, 2004, 27:319–340.Google Scholar
  11. [11]
    Frey W H. Mesh relaxation: a new technique for improving triangulations[J]. International Journal for Numerical Methods in Engineering, 1991, 31:1121–1133.zbMATHCrossRefGoogle Scholar
  12. [12]
    Borouchaki H, George P L, Mohammadi B. Delaunay mesh generation governed by metric specifications, part II, application[J]. Finite Elements in Analysis and Design, 1997, 25:85–109.zbMATHCrossRefGoogle Scholar
  13. [13]
    White F M. Viscous fluid flow[M]. 3rd Ed, McGraw-Hill, 2005.Google Scholar
  14. [14]
    Williamson C H K. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers[J]. Journal of Fluid Mechanics, 1989, 206:579–627.CrossRefGoogle Scholar
  15. [15]
    Braza M, Chassaing P, Ha Minh H. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder[J]. Journal of Fluid Mechanics, 1986, 165:79–130.zbMATHCrossRefGoogle Scholar
  16. [16]
    Karniadakis G E, Triantafyllou G S. A passive control of vortex shedding in the wake of a circular cylinder[J]. Journal of Fluid Mechanics, 1989, 199:441–469.zbMATHCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Suthee Traivivatana
    • 1
  • Parinya Boonmarlert
    • 1
  • Patcharee Theeraek
    • 1
  • Sutthisak Phongthanapanich
    • 2
  • Pramote Dechaumphai
    • 1
    Email author
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringChulalongkorn UniversityPatumwan, BangkokThailand
  2. 2.Department of Mechanical Engineering Technology, College of Industrial TechnologyKing Mongkut’s Institute of Technology North BangkokBangsue, BangkokThailand

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