Skip to main content

Mixed Order Mesh Curving

  • Chapter
  • First Online:
Mesh Generation and Adaptation

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 30))


Linear hybrid unstructured meshes are elevated to mixed-order meshes in response to geometry curvature. The linear meshes are elevated to the required degree on an element-by-element basis in regions of high geometry curvature. Weighted condition number mesh smoothing is used to untangle and improve the quality of the current mixed-order mesh. Periodically the mesh is tested for additional element elevation using a deviation criterion. Once the mesh smoothing is complete the mesh can be exported as a mixed order mesh or uniformly elevated to the desired degree. Details of the mesh elevation and smoothing process are described. Two three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality mixed-order meshes.

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. 1.

    The intended application of this technique is mesh curving on NURB geometric surfaces but does not preclude use of discrete surfaces.

  2. 2.

    The highest surface and volume element degree will be Q4 even if the surface polynomial degree is higher.


  1. Chen, C.H.: A Radial Basis Functions Approach to Generating High-Order Curved Element Meshes for Computational Fluid Dynamics. Master’s thesis, Imperial College, London (2013)

    Google Scholar 

  2. Stees, M., Shontz, S.M.: Spectral and High Order Methods for Partial Differential Equations, p. 229 (2018)

    Google Scholar 

  3. Ims, J., Duan, Z., Wang, Z.J.: In: 22nd AIAA Computational Fluid Dynamics Conference (AIAA 2015-2293)

    Google Scholar 

  4. Persson, P.O., Peraire, J.: In: 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition (AIAA 2009-0949).

  5. Moxey, D., Ekelschot, D., Keskin, Ü., Sherwin, S.J., Peiró, J.: Comput. Aided Des. 72, 130 (2016).

    Article  Google Scholar 

  6. Fortunato, M., Persson, P.O.: J. Comput. Phys. 307, 1 (2016)

    Article  MathSciNet  Google Scholar 

  7. Feuillet, R., Loseille, A., Alauzet, F.: In: International Meshing Roundtable, pp. 3–21 Springer, Berlin (2018)

    Google Scholar 

  8. Zhang, R., Johnen, A., Remacle, J.F.: In: International Meshing Roundtable, pp. 57–69. Springer, Berlin (2018)

    Google Scholar 

  9. Ruiz-Gironés, E., Sarrate, J., Roca, X.: Procedia Eng. 163, 315 (2016)

    Article  Google Scholar 

  10. Karman, S.L., Erwin, J.T., Glasby, R.S., Stefanski, D.: In: 46th AIAA fluid dynamics conference (AIAA 2016-3178), p. 3178.

  11. Karman, S.L.: In: International Conference on Spectral and High Order Methods (2018)

    Google Scholar 

  12. Karman, S.L.: In: International Meshing Roundtable, pp. 303–325. Springer, Berlin (2018)

    Google Scholar 

  13. Geuzaine, C., Remacle, J.F.: Gmsh.

  14. Nektar++: Nekmesh.

  15. Pointwise Inc.: Pointwise.

  16. Computational geometry kernel support. U. S. Air Force contract FA9101-18-P-0042, Topic AF181-015

    Google Scholar 

  17. Karman, S.L.: In: AIAA Aviation 2019 Forum (AIAA 2019-3317), p. 3317

    Google Scholar 

  18. Aubert, P., Di Césaré, N., Pironneau, O.: Comput. Vis. Sci. 3(4), 197 (2001)

    Article  Google Scholar 

  19. 3rd AIAA Geometry and Mesh Generation Workshop.

  20. 4th AIAA High Lift Prediction Workshop.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Carolyn D. Woeber .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Cadence Design Systems, Inc. under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Karman, S.L., Karman-Shoemake, K., Woeber, C.D. (2022). Mixed Order Mesh Curving. In: Sevilla, R., Perotto, S., Morgan, K. (eds) Mesh Generation and Adaptation. SEMA SIMAI Springer Series, vol 30. Springer, Cham.

Download citation

Publish with us

Policies and ethics