Skip to main content
SpringerLink
Log in

Comparison of mapping operators for unstructured meshes

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

In this paper, two PDE-based mapping operators for the generation of unstructured meshes are compared. While the Winslow operator allows the construction of valid meshes for most configurations, the functional-based operators based on area, length, orthogonality and their combinations provide a finer control on the resulting meshes. Two distinct discretization methods of the operators are also compared. An original approach using a finite difference scheme on unstructured meshes is implemented and compared to a finite volume formulation. While more complex to implement and control, mainly because of the cross-derivative terms which must be carefully discretized, the finite volume method yields a more robust and stable formulation that allows dealing with sharp curvature variations of the boundaries. Finally, a criterion for the mesh smoothness which has a global definition is presented in order to compare the smoothness of the resulting mesh obtained by different operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Anderson DA (1987) An adaptive grid scheme controlling cell area/volume. In: AIAA 25th Aerospace Science Meeting

  2. Anderson DA (1987) Equidistribution schemes, poisson generators, and adaptive grids. Appl Math Comput 24:211–227

    Article  MATH  MathSciNet  Google Scholar 

  3. Spekreijse S (1995) Elliptic generation based on laplace equations and algebraic transformations. J Comput Phys 118:38–61

    Article  MATH  Google Scholar 

  4. Spekreijse S (1996) Elliptic generation systems. Technical Report NLR TP 96735. National Aerospace Laboratory NLR

  5. Garon A (1983) Génération de maillages sur des surfaces et résolution numérique des équations de navier-stokes dans une cascade. Master’s Thesis, École polytechnique de Montréal

  6. Khamayseh A, Mastin C (1996) Computational conformal mapping for surface grid generation. J Comput Phys 123:394–401

    Article  MATH  MathSciNet  Google Scholar 

  7. Khamayseh A, Hansen G (2000) Quasi-orthogonal grids with impedance matching. SIAM J Sci Comput 22:1220–1237

    Article  MATH  MathSciNet  Google Scholar 

  8. Villamizar V, Acosta S (2009) Elliptic grids with nearly uniform cell area and line spacing. Electron Trans Numer Anal, pp 59–75

  9. Villamizar V, Weber M (2007) Boundary-conforming coordinates with grid line control for acoustic scattering from complexly shaped obstacles. Wiley InterScience (20235)

  10. Azarenok B (2009) Generation of structured difference grids in two-dimensional nonconvex domains using mappings. J Comput Math Math Phys 49(5):797–809

    Article  MathSciNet  Google Scholar 

  11. Castillo J, Steinberg S, Roache P (1988) On the folding of numerically generated grids: use of reference grid. J Commun Appl Numer Methods 4:471–481

    Article  MATH  MathSciNet  Google Scholar 

  12. Knupp P, Steinberg S (1993) Fundamentals of grid generation. CRC Press, Boca Raton ISBN 0-8493-8987-9

  13. Chibisov D, Ganzha V, Mayr E, Vorozhtsov E (2006) On the provable tight approximation of optimal meshing for non-convex regions. Computational topology and geometry in application of computer algebra (ACA2006), Varna, Bulgaria

  14. Khattri S (2007) Grid generation and adaptation by functionals. J Comput Appl Math 26(2):235–249

    MATH  MathSciNet  Google Scholar 

  15. Winslow AM (1967) Numerical solution of the quasilinear Poisson equations in a nonuniform triangle mesh. J Comput Phys 2:149–172

    MathSciNet  Google Scholar 

  16. Knupp PM (1999) Winslow smoothing on two-dimensional unstructured meshes. Eng Comput 15(3):263–268

    Article  MATH  Google Scholar 

  17. Winslow AM (1997) Numerical solution of the quasi-linear Poisson equation in a non-uniform triangular mesh. J Comput Phys 135:128–138

    Article  MATH  MathSciNet  Google Scholar 

  18. Karman S (2010) Virtual control volumes for two dimensional unstructured elliptic smoothing. In: Proceedings of the 19th International Meshing Roundtable, Sandia National Laboratory, Chattanooga, TN, pp 121–142

Download references

Author information

Authors and Affiliations

  1. École Polytechnique de Montréal, 2900 boul. Édouard-Montpetit, Campus de l’Université de Montréal, 2500 chemin de Polytechnique, Montreal, QC, H3T 1J4, Canada

    Sina Arabi, Ricardo Camarero & François Guibault

Authors
  1. Sina Arabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Camarero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. François Guibault
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sina Arabi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arabi, S., Camarero, R. & Guibault, F. Comparison of mapping operators for unstructured meshes. Engineering with Computers 31, 579–595 (2015). https://doi.org/10.1007/s00366-014-0361-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-014-0361-2

Keywords

Search

Navigation