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An unstructured staggered scheme for the Navier—Stokes equations

  • I. Wenneker
  • G. Segal
  • P. Wesseling
Conference paper

Summary

A novel scheme for viscous incompressible flows on unstructured grids is introduced. A staggered positioning of the variables is used: the pressure is located in the centroids of the triangles while the normal velocity components are placed at the midpoints of the faces of the triangles. The pressure-correction approach is employed to deal with the divergence-freedom constraint of the velocity. Spatial discretization is discussed. For the lid-driven cavity problem, good results are obtained.

Keywords

Spatial Discretization Compressible Flow Unstructured Grid Primary Vortex Viscous Incompressible Flow 
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.

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References

  1. [1]
    Ghia, U., Ghia, K.N., Shin, C.T. (1982): High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48, 387–411MATHCrossRefGoogle Scholar
  2. [2]
    Harlow, F.H., Welch, J.E. (1965): Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182–2189MATHCrossRefGoogle Scholar
  3. [3]
    van der Heul, D.R., Vuik, C, Wesseling, P. (2002): A conservative pressure-correction method for the Euler and ideal MHD equations at all speeds. Internat. J. Numer. Methods Fluids 40, 521–529MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Nicolaides, R.A., Porsching, T.A., Hall, C.A. (1995): Covolume methods in computational fluid dynamics. In: Hafez, M.M., Oshima, K. (eds.): Computational fluid dynamics review 1995. Wiley, Chichester, pp. 279–299Google Scholar
  5. [5]
    Perot, B. (2000): Conservation properties of unstructured staggered mesh schemes. J. Comput. Phys. 159, 58–89MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Rhie, C.M., Chow, W.L. (1983): Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21, 1525–1532MATHCrossRefGoogle Scholar
  7. [7]
    Sohn, J.L. (1988): Evaluation of FIDAP on some classical laminar and turbulent benchmarks. Internat. J. Numer. Methods Fluids 8, 1469–1490CrossRefGoogle Scholar
  8. [8]
    Wenneker, I., Segal, A., Wesseling, P. (2000): Computation of compressible flows on unstructured staggered grids. In: ECCOMAS 2000. Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering. CIMNE, Barcelona. CD-RomGoogle Scholar
  9. [9]
    Wenneker, I., Segal, A., Wesseling, P. (2001): A Mach-uniform unstructured staggered grid method. Internat. J. Numer. Methods Fluids, submittedGoogle Scholar
  10. [10]
    Wenneker, I., Segal, A., Wesseling, P. (2003): Conservation properties of a new unstructured staggered scheme. Comput. & Fluids 32, 139–147MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Wesseling, P., Segal, A., Kassels, C.G.M., Bijl, H. (1998): Computing flows on general two-dimensional nonsmooth staggered grids. J. Engrg. Math. 34, 21–44MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Wesseling, P., Segal A., Kassels, C.G.M. (1999): Computing flows on general three-dimensional nonsmooth staggered grids, J. Comput. Phys. 149, 333–362MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Wesseling, P. (2001): Principles of computational fluid dynamics. Springer, BerlinCrossRefGoogle Scholar
  14. [14]
    Wesseling, P., van der Heul, D.R. (2001): Uniformly effective numerical methods for hyperbolic systems. Computing 66, 249–267MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • I. Wenneker
    • 1
  • G. Segal
    • 1
  • P. Wesseling
    • 1
  1. 1.Delft University of TechnologyDelftNetherlands

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