Skip to main content
Erschienen in: Engineering with Computers 1/2005

01.11.2005 | Original Article

A local cell quality metric and variational grid smoothing algorithm

verfasst von: L. Branets, G. F. Carey

Erschienen in: Engineering with Computers | Ausgabe 1/2005

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A local cell quality metric is introduced and used to construct a variational functional for a grid smoothing algorithm. A maximum principle is proved and the properties of the local quality measure, which combines element shape and size control metrics, are investigated. Level set contours are displayed to indicate the effect of cell distortion. The approach is demonstrated for meshes of triangles and quadrilaterals in 2D and a test case with hexahedral cells in 3D. Issues such as the use of a penalty for folded meshes and the effect of valence change in the mesh patches are considered.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Winslow AM (1967) Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J Comput Phys 2:149–172MathSciNet Winslow AM (1967) Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh. J Comput Phys 2:149–172MathSciNet
2.
3.
Zurück zum Zitat Charakhch’yan AA, Ivanenko SA (1997) A variational form of the Winslow grid generator. J Comput Phys 136:385–398MathSciNetCrossRef Charakhch’yan AA, Ivanenko SA (1997) A variational form of the Winslow grid generator. J Comput Phys 136:385–398MathSciNetCrossRef
4.
Zurück zum Zitat Carey GF (1997) Computational grids: generation, adaptation and solution strategies. Taylor and Francis Carey GF (1997) Computational grids: generation, adaptation and solution strategies. Taylor and Francis
5.
Zurück zum Zitat Liseikin VD (1999) Grid generation methods. Springer, Berlin Heidelberg New YorkMATH Liseikin VD (1999) Grid generation methods. Springer, Berlin Heidelberg New YorkMATH
6.
Zurück zum Zitat Pardhanani A, Carey GF (1988) Optimization of computational grids. Numerical Methods Partial Differential Equations 4:95–117CrossRefMATHMathSciNet Pardhanani A, Carey GF (1988) Optimization of computational grids. Numerical Methods Partial Differential Equations 4:95–117CrossRefMATHMathSciNet
7.
Zurück zum Zitat Garanzha VA (2000) Barrier variational generation of quasi-isometric grids. Comput Math Math Phys 40:1617–1637MATHMathSciNet Garanzha VA (2000) Barrier variational generation of quasi-isometric grids. Comput Math Math Phys 40:1617–1637MATHMathSciNet
8.
Zurück zum Zitat Courant R (1977) Dirichlet’s principle, conformal mappings and minimal surfaces. Springer, Berlin Heidelberg New York Courant R (1977) Dirichlet’s principle, conformal mappings and minimal surfaces. Springer, Berlin Heidelberg New York
9.
Zurück zum Zitat Jacquotte OP (1987) A mechanical model for a new grid generation method in computational fluid dynamics. Comput Meth Appl Mech Eng 66:323–338CrossRefMathSciNet Jacquotte OP (1987) A mechanical model for a new grid generation method in computational fluid dynamics. Comput Meth Appl Mech Eng 66:323–338CrossRefMathSciNet
11.
Zurück zum Zitat Branets LV, Garanzha VA (2001) Global condition number of trilinear mapping. Application to 3D grid generation. In: Proceedings of the minisymposium in the international conference “Optimization of finite-element approximations, splines and wavelets”, 25–29 June 2001, St.-Petersburg Branets LV, Garanzha VA (2001) Global condition number of trilinear mapping. Application to 3D grid generation. In: Proceedings of the minisymposium in the international conference “Optimization of finite-element approximations, splines and wavelets”, 25–29 June 2001, St.-Petersburg
12.
Zurück zum Zitat Field DA (2000) Qualitative measures for initial meshes. Int J Numerical Methods Eng 47:887–906CrossRefMATH Field DA (2000) Qualitative measures for initial meshes. Int J Numerical Methods Eng 47:887–906CrossRefMATH
14.
Zurück zum Zitat Lee CK, Lo SH (1994) A new scheme for the generation of a graded quadrilateral mesh. Comput Struct 52:847–857CrossRefMATH Lee CK, Lo SH (1994) A new scheme for the generation of a graded quadrilateral mesh. Comput Struct 52:847–857CrossRefMATH
16.
Zurück zum Zitat Branets L, Carey GF (2004) Smoothing and adaptive redistribution for grids with irregular valence and hanging nodes. In: Proceedings of the 13th international meshing roundtable, Williamsburg, p 333–344 Branets L, Carey GF (2004) Smoothing and adaptive redistribution for grids with irregular valence and hanging nodes. In: Proceedings of the 13th international meshing roundtable, Williamsburg, p 333–344
17.
Zurück zum Zitat Branets L, Carey GF (2005) Extension of a mesh quality metric for elements with a curved boundary edge or surface. J Comp Infor Sci Eng 5(4):to appear Branets L, Carey GF (2005) Extension of a mesh quality metric for elements with a curved boundary edge or surface. J Comp Infor Sci Eng 5(4):to appear
Metadaten
Titel
A local cell quality metric and variational grid smoothing algorithm
verfasst von
L. Branets
G. F. Carey
Publikationsdatum
01.11.2005
Verlag
Springer-Verlag
Erschienen in
Engineering with Computers / Ausgabe 1/2005
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-005-0309-7

Weitere Artikel der Ausgabe 1/2005

Engineering with Computers 1/2005 Zur Ausgabe