Skip to main content
Top
Published in: Engineering with Computers 3/2016

01-07-2016 | Original Article

Improving the quality of finite volume meshes through genetic optimisation

Authors: B. Fabritius, G. Tabor

Published in: Engineering with Computers | Issue 3/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Mesh quality issues can have a substantial impact on the solution process in Computational Fluid Dynamics, leading to poor quality solutions, hindering convergence and in some cases, causing the solution to diverge. In many areas of application, there is an interest in automated generation of finite volume meshes, where a meshing algorithm controlled by pre-specified parameters is applied to a pre-existing CAD geometry. In such cases, the user is typically confronted with a large number of controllable parameters, and adjusting these takes time and perseverance. The process can, however, be regarded as a multi-input and possibly multi-objective optimisation process which can be optimised by application of Genetic Algorithm techniques. We have developed a GA optimisation code in the language Python, including an implementation of the NGSA-II multi-objective optimisation algorithm, and applied to control the mesh generation process using the snappyHexMesh automated mesher in OpenFOAM. We demonstrate the results on three selected cases, demonstrating significant improvement in mesh quality in all cases.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Literature
1.
go back to reference Abe K, Ohtsuka T (1984) Some salient features of the time-averaged ground vehicle wake. In: Technical report SAE-paper 840300. SAE, Warrendale Abe K, Ohtsuka T (1984) Some salient features of the time-averaged ground vehicle wake. In: Technical report SAE-paper 840300. SAE, Warrendale
2.
go back to reference Baker M, Daniels S, Young P, Tabor G (2014) Investigation of ow through a computationally generated packed column using CFD and additive layer manufacturing. Comput Chem Eng 67:159–165CrossRef Baker M, Daniels S, Young P, Tabor G (2014) Investigation of ow through a computationally generated packed column using CFD and additive layer manufacturing. Comput Chem Eng 67:159–165CrossRef
3.
go back to reference Baker MJ, Tabor GR (2010) Computational analysis of transitional airflow through packed columns of spheres using the finite volume technique. Comput Chem Eng 34:878–885CrossRef Baker MJ, Tabor GR (2010) Computational analysis of transitional airflow through packed columns of spheres using the finite volume technique. Comput Chem Eng 34:878–885CrossRef
4.
go back to reference Behzadian K, Kapelan Z, Savic D, Ardeshir A (2009) Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks. Environ Model Softw 24:530–541CrossRef Behzadian K, Kapelan Z, Savic D, Ardeshir A (2009) Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks. Environ Model Softw 24:530–541CrossRef
5.
go back to reference Berzins M (1999) Mesh quality: a function of geometry, error estimates, or both? Eng Comput 15(3):236–247CrossRefMATH Berzins M (1999) Mesh quality: a function of geometry, error estimates, or both? Eng Comput 15(3):236–247CrossRefMATH
6.
go back to reference Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395CrossRef Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395CrossRef
7.
go back to reference Diskin B, Thomas J (2012) Effects of mesh regularity on accuracy of finite-volume schemes. In: 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 2012-0609. AIAA, New York Diskin B, Thomas J (2012) Effects of mesh regularity on accuracy of finite-volume schemes. In: 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 2012-0609. AIAA, New York
8.
go back to reference Field D (1988) Laplacian smoothing and Delaunay triangulations. Commun Numer Methods 4:709–712CrossRefMATH Field D (1988) Laplacian smoothing and Delaunay triangulations. Commun Numer Methods 4:709–712CrossRefMATH
9.
go back to reference Field D (2000) Qualitative measures for initial meshes. Int J Numer Methods Eng 47:887–906CrossRefMATH Field D (2000) Qualitative measures for initial meshes. Int J Numer Methods Eng 47:887–906CrossRefMATH
10.
go back to reference Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3:1–16CrossRef Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3:1–16CrossRef
11.
go back to reference Freitag L (2001) Local optimization-based untangling algorithms for quadrilateral meshes. In: Proceedings of the 10th international meshing roundtable, Newport Beach, pp 397–406. Sandia National Laboratories, New Mexico Freitag L (2001) Local optimization-based untangling algorithms for quadrilateral meshes. In: Proceedings of the 10th international meshing roundtable, Newport Beach, pp 397–406. Sandia National Laboratories, New Mexico
12.
go back to reference Freitag L, Jones M, Plassmann P (1999) A parallel algorithm for mesh smoothing. SIAM J Sci Comput 20(6):2023–2040 Freitag L, Jones M, Plassmann P (1999) A parallel algorithm for mesh smoothing. SIAM J Sci Comput 20(6):2023–2040
13.
go back to reference Gagné C, Parizeau M (2006) Genericity in evolutionary computation software tools; principles and case-study. Int J Artif Intell Tools 15(2):173–194CrossRef Gagné C, Parizeau M (2006) Genericity in evolutionary computation software tools; principles and case-study. Int J Artif Intell Tools 15(2):173–194CrossRef
14.
go back to reference Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York
15.
go back to reference Hinterberger C, Garca-Villalba M, Rodi W (2004) Large eddy simulation of flow around the Ahmed body. In: McCallen JRR, Browand F (eds) Lecture notes in applied and computational mechanics/the aerodynamics of heavy vehicles: trucks, buses, and trains. Springer, New York Hinterberger C, Garca-Villalba M, Rodi W (2004) Large eddy simulation of flow around the Ahmed body. In: McCallen JRR, Browand F (eds) Lecture notes in applied and computational mechanics/the aerodynamics of heavy vehicles: trucks, buses, and trains. Springer, New York
16.
go back to reference Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Imperial College Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Imperial College
17.
go back to reference Jeng Y, Chen J (1992) Truncation error analysis of the finite volume method for a model steady convective equation. J Comput Phys 100:64–76 Jeng Y, Chen J (1992) Truncation error analysis of the finite volume method for a model steady convective equation. J Comput Phys 100:64–76
18.
go back to reference Jourdan L, Corne D, Savic D, Walters G (2005) Preliminary investigation of the learnable evolution model for faster/better multiobjective water systems design. In: Proceedings of the third international conference on evolutionary multi-criterion optimization, EMO 05 Jourdan L, Corne D, Savic D, Walters G (2005) Preliminary investigation of the learnable evolution model for faster/better multiobjective water systems design. In: Proceedings of the third international conference on evolutionary multi-criterion optimization, EMO 05
19.
go back to reference Kallinderis Y, Kontzialis C (2009) A priori mesh quality estimation via direct relation between truncation error and mesh distortion. J Comput Phys 228:881–902 Kallinderis Y, Kontzialis C (2009) A priori mesh quality estimation via direct relation between truncation error and mesh distortion. J Comput Phys 228:881–902
20.
go back to reference Knupp P (2000) Achieving finite element mesh quality via optimization of the Jacobian matric norm and associated quantities. Part 1. A framework for surface mesh optimization. Int J Numer Methods Eng 48:401–420 Knupp P (2000) Achieving finite element mesh quality via optimization of the Jacobian matric norm and associated quantities. Part 1. A framework for surface mesh optimization. Int J Numer Methods Eng 48:401–420
21.
go back to reference Knupp P (2000) Achieving finite element mesh quality via optimization of the Jacobian matric norm and associated quantities. Part 2. A framework for volume mesh optimization. Int J Numer Methods Eng 48:1165–1185 Knupp P (2000) Achieving finite element mesh quality via optimization of the Jacobian matric norm and associated quantities. Part 2. A framework for volume mesh optimization. Int J Numer Methods Eng 48:1165–1185
23.
go back to reference Knupp P (2003) Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem Anal Des 39:217–241CrossRefMATH Knupp P (2003) Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem Anal Des 39:217–241CrossRefMATH
24.
go back to reference Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 2: Understanding the flow. J Fluids Eng 127(5):919–928 Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 2: Understanding the flow. J Fluids Eng 127(5):919–928
25.
go back to reference Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 1: Large Eddy simulations. J Fluids Eng 127(5):907–918 Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 1: Large Eddy simulations. J Fluids Eng 127(5):907–918
26.
go back to reference Lienhart H, Becker S (2003) Flow and turbulence structure in the wake of a simplified car model. In: SAE 2003 world congress, Detroit Lienhart H, Becker S (2003) Flow and turbulence structure in the wake of a simplified car model. In: SAE 2003 world congress, Detroit
27.
go back to reference Lienhart H, Stoots C, Becker S (2000) Flow and turbulence structures in the wake of a simplified car model (Ahmed model). In: DGLR Fach symposium der AG STAB, Stuttgart University Lienhart H, Stoots C, Becker S (2000) Flow and turbulence structures in the wake of a simplified car model (Ahmed model). In: DGLR Fach symposium der AG STAB, Stuttgart University
28.
go back to reference McRae D, Laflin K (1999) Dynamic grid adaption and grid quality. In: Thompson J, Soni B, Weatherhill N (eds) Handbook of grid generation, chap 34. CRC Press, London McRae D, Laflin K (1999) Dynamic grid adaption and grid quality. In: Thompson J, Soni B, Weatherhill N (eds) Handbook of grid generation, chap 34. CRC Press, London
29.
go back to reference Message Passing Interface Forum (2009) MPI: a message-passing interface standard, version 2.2. High-Performance Computing Center, Stuttgart Message Passing Interface Forum (2009) MPI: a message-passing interface standard, version 2.2. High-Performance Computing Center, Stuttgart
30.
go back to reference Michalewicz Z (1996) Genetic algorithms \(+\) data structures \(=\) evolution programs. Springer, BerlinCrossRefMATH Michalewicz Z (1996) Genetic algorithms \(+\) data structures \(=\) evolution programs. Springer, BerlinCrossRefMATH
31.
go back to reference Minguez M, Pasquetti R, Serre E (2008) High-order large-Eddy simulation of flow over the ’Ahmed body’ car model. Phys Fluids 20(9):095101 Minguez M, Pasquetti R, Serre E (2008) High-order large-Eddy simulation of flow over the ’Ahmed body’ car model. Phys Fluids 20(9):095101
33.
go back to reference Pagnutti D, Ollivier-Gooch C (2010) Two-dimensional Delaunay-based anisotropic mesh adaption. Eng Comput 26:407–418CrossRef Pagnutti D, Ollivier-Gooch C (2010) Two-dimensional Delaunay-based anisotropic mesh adaption. Eng Comput 26:407–418CrossRef
34.
go back to reference Parthasarathy V, Graichen C, Hathaway A (1993) A comparison of tetrahedron quality measures. Finite Elem Anal Des 15:255–261CrossRef Parthasarathy V, Graichen C, Hathaway A (1993) A comparison of tetrahedron quality measures. Finite Elem Anal Des 15:255–261CrossRef
35.
go back to reference Robinson J (1994) Quadrilateral and hexahedron shape parameters. Finite Elem Anal Des 16:43–52CrossRefMATH Robinson J (1994) Quadrilateral and hexahedron shape parameters. Finite Elem Anal Des 16:43–52CrossRefMATH
36.
go back to reference Shepherd JF, Johnson CR (2008) Hexahedral mesh generation constraints. Eng Comput 24(3):195–213CrossRef Shepherd JF, Johnson CR (2008) Hexahedral mesh generation constraints. Eng Comput 24(3):195–213CrossRef
37.
go back to reference Srinivas N, Deb K (1995) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248CrossRef Srinivas N, Deb K (1995) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248CrossRef
38.
go back to reference Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics : the finite volume method. Longman Scientific & Technical, New York Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics : the finite volume method. Longman Scientific & Technical, New York
39.
go back to reference Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object orientated techniques. Comput Phys 12(6):620–631CrossRef Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object orientated techniques. Comput Phys 12(6):620–631CrossRef
40.
go back to reference Zang Y, Street RL, Koseff JR (1994) A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J Comput Phys 114(1):18–33MathSciNetCrossRefMATH Zang Y, Street RL, Koseff JR (1994) A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J Comput Phys 114(1):18–33MathSciNetCrossRefMATH
41.
go back to reference Zitzler E, Laumanns M, Bleuler S (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195CrossRef Zitzler E, Laumanns M, Bleuler S (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195CrossRef
Metadata
Title
Improving the quality of finite volume meshes through genetic optimisation
Authors
B. Fabritius
G. Tabor
Publication date
01-07-2016
Publisher
Springer London
Published in
Engineering with Computers / Issue 3/2016
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-015-0423-0

Other articles of this Issue 3/2016

Engineering with Computers 3/2016 Go to the issue