Advertisement

Curvilinear Mesh Generation for Boundary Layer Problems

  • D. Moxey
  • M. Hazan
  • S. J. Sherwin
  • J. Peiro
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 128)

Abstract

In this article, we give an overview of a new technique for unstructured curvilinear boundary layer grid generation, which uses the isoparametric mappings that define elements in an existing coarse prismatic grid to produce a refined mesh capable of resolving arbitrarily thin boundary layers. We demonstrate that the technique always produces valid grids given an initially valid coarse mesh, and additionally show how this can be extended to convert hybrid meshes to meshes containing only simplicial elements.

Keywords

Mesh Generation Subdivision Strategy Polynomial Space Thin Boundary Layer Boundary Layer Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall (1976)Google Scholar
  2. 2.
    Dey, S., O’Bara, R.M., Shephard, M.: Curvilinear mesh generation in 3D. In: Proceedings of the 8th International Meshing Roundtable, South Lake Tahoe, California (1999)Google Scholar
  3. 3.
    Dompierre, J., Labbé, P., Vallet, M.-G., Camarero, R.: How to subdivide pyramids, prisms and hexahedra into tetrahedra. In: 8th International Meshing Roundtable, Lake Tahoe, California, October 10–13 (1999)Google Scholar
  4. 4.
    Gargallo-Peiró, A., Roca, X., Sarrate, J., Peraire, J.: Inserting curved boundary layers for viscous flow simulation with high-order tetrahedra. In: 22nd International Meshing Roundtable (2013)Google Scholar
  5. 5.
    Geuzaine, C., Remacle, J.-F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79(11), 1309–1331 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Gordon, W.J., Hall, C.A.: Construction of curvilinear co-ordinate systems and applications to mesh generation. International Journal for Numerical Methods in Engineering 7(4), 461–477 (1973)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Karniadakis, G.E., Sherwin, S.J.: Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press (2005)Google Scholar
  8. 8.
    Mavriplis, D.J.: Unstructured grid techniques. Annual Review of Fluid Mechanics 29, 473–514 (1997)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Moxey, D., Hazan, M., Peiró, J., Sherwin, S.J.: On the generation of curvilinear meshes through subdivision of isoparametric elements. To Appear in Proceedings of Tetrahedron IV (2014)Google Scholar
  10. 10.
    Moxey, D., Hazan, M., Sherwin, S.J., Peiró, J.: An isoparametric approach to high-order curvilinear boundary-layer meshing. Under Review in Comp. Meth. App. Mech. Eng. (2014)Google Scholar
  11. 11.
    Peiró, J., Sayma, A.I.: A 3-D unstructured multigrid Navier-Stokes solver. In: Morton, K.W., Baines, M.J. (eds.) Numerical Methods for Fluid Dynamics V. Oxford University Press (1995)Google Scholar
  12. 12.
    Peraire, J., Morgan, K.: Unstructured mesh generation including directional refinement for aerodynamic flow simulation. Finite Elements in Analysis and Design 25, 343–356 (1997)CrossRefzbMATHGoogle Scholar
  13. 13.
    Peraire, J., Peiró, J., Morgan, K.: Multigrid solution of the 3-D compressible Euler equations on unstructured tetrahedral grids. International Journal for Numerical Methods in Engineering 36, 1029–1044 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Persson, P.-O., Peraire, J.: Curved mesh generation and mesh refinement using Lagrangian solid mechanics. In: 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando (FL), USA, January 5–9. AIAA paper 2009–949 (2009)Google Scholar
  15. 15.
    Pirzadeh, S.: Three-dimensional unstructured viscous grids by the advancing-layers method. AIAA Journal 34(1), 43–49 (1996)CrossRefzbMATHGoogle Scholar
  16. 16.
    Sahni, O., Luo, X.J., Jansen, K.E., Shepard, M.S.: Curved boundary layer meshing for adaptive viscous flow simulations. Finite Elements in Analysis and Design 46(1-2), 132–139 (2010)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Schlichting, H.: Boundary-layer theory, 7th edn. McGraw-Hill (1979)Google Scholar
  18. 18.
    Schmitt, V., Charpin, F.: Pressure distributions on the ONERA-M6 wing at transonic mach numbers. In: Experimental Data Base for Computer Program Assessment, AGARD AR 138. Report of the Fluid Dynamics Panel Working Group 04 (May 1979)Google Scholar
  19. 19.
    Sherwin, S.J., Peiró, J.: Mesh generation in curvilinear domains using high-order elements. International Journal for Numerical Methods in Engineering 53(1), 207–223 (2002)CrossRefzbMATHGoogle Scholar
  20. 20.
    Toulorge, T., Geuzaine, C., Remacle, J.-F., Lambrechts, J.: Robust untangling of curvilinear meshes. Journal of Computational Physics 254, 8–26 (2013)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Xie, Z.Q., Sevilla, R., Hassan, O., Morgan, K.: The generation of arbitrary order curved meshes for 3D finite element analysis. Computational Mechanics 51(3), 361–374 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Zienkiewicz, O.C., Phillips, D.V.: An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates. International Journal for Numerical Methods in Engineering 3(4), 519–528 (1971)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of AeronauticsImperial College LondonLondonUK

Personalised recommendations