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Improving the quality of finite volume meshes through genetic optimisation

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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.

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Notes

  1. http://openfoamwiki.net/index.php/Contrib_PyFoam.

References

  1. Abe K, Ohtsuka T (1984) Some salient features of the time-averaged ground vehicle wake. In: Technical report SAE-paper 840300. SAE, Warrendale

  2. 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 67:159–165

    Article  Google Scholar 

  3. Baker MJ, Tabor GR (2010) Computational analysis of transitional airflow through packed columns of spheres using the finite volume technique. Comput Chem Eng 34:878–885

    Article  Google Scholar 

  4. 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 24:530–541

    Article  Google Scholar 

  5. Berzins M (1999) Mesh quality: a function of geometry, error estimates, or both? Eng Comput 15(3):236–247

    Article  MATH  Google Scholar 

  6. Deb K, Anand A, Joshi D (2002) A computationally efficient evolutionary algorithm for real-parameter optimization. Evol Comput 10(4):371–395

    Article  Google Scholar 

  7. 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. Field D (1988) Laplacian smoothing and Delaunay triangulations. Commun Numer Methods 4:709–712

    Article  MATH  Google Scholar 

  9. Field D (2000) Qualitative measures for initial meshes. Int J Numer Methods Eng 47:887–906

    Article  MATH  Google Scholar 

  10. Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3:1–16

    Article  Google Scholar 

  11. 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. Freitag L, Jones M, Plassmann P (1999) A parallel algorithm for mesh smoothing. SIAM J Sci Comput 20(6):2023–2040

  13. Gagné C, Parizeau M (2006) Genericity in evolutionary computation software tools; principles and case-study. Int J Artif Intell Tools 15(2):173–194

    Article  Google Scholar 

  14. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York

  15. 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. Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Imperial College

  17. 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. 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. 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. 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. 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

  22. Knupp P (2001) Algebraic mesh quality metrics. SIAM J Sci Comput 23(1):192–218

    Article  MathSciNet  MATH  Google Scholar 

  23. Knupp P (2003) Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem Anal Des 39:217–241

    Article  MATH  Google Scholar 

  24. Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 2: Understanding the flow. J Fluids Eng 127(5):919–928

  25. Krajnovic S, Davidson L (2005) Flow around a simplified car. Part 1: Large Eddy simulations. J Fluids Eng 127(5):907–918

  26. Lienhart H, Becker S (2003) Flow and turbulence structure in the wake of a simplified car model. In: SAE 2003 world congress, Detroit

  27. 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. 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. Message Passing Interface Forum (2009) MPI: a message-passing interface standard, version 2.2. High-Performance Computing Center, Stuttgart

  30. Michalewicz Z (1996) Genetic algorithms \(+\) data structures \(=\) evolution programs. Springer, Berlin

    Book  MATH  Google Scholar 

  31. 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

  32. Owen SJ, Shelton TR (2014) Evaluation of grid-based hex meshes for solid mechanics. Eng Comput 1–15. doi:10.1007/s00366-014-0368-8

  33. Pagnutti D, Ollivier-Gooch C (2010) Two-dimensional Delaunay-based anisotropic mesh adaption. Eng Comput 26:407–418

    Article  Google Scholar 

  34. Parthasarathy V, Graichen C, Hathaway A (1993) A comparison of tetrahedron quality measures. Finite Elem Anal Des 15:255–261

    Article  Google Scholar 

  35. Robinson J (1994) Quadrilateral and hexahedron shape parameters. Finite Elem Anal Des 16:43–52

    Article  MATH  Google Scholar 

  36. Shepherd JF, Johnson CR (2008) Hexahedral mesh generation constraints. Eng Comput 24(3):195–213

    Article  Google Scholar 

  37. Srinivas N, Deb K (1995) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

  38. Versteeg HK, Malalasekera W (1995) An introduction to computational fluid dynamics : the finite volume method. Longman Scientific & Technical, New York

  39. Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object orientated techniques. Comput Phys 12(6):620–631

    Article  Google Scholar 

  40. 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):18–33

    Article  MathSciNet  MATH  Google Scholar 

  41. Zitzler E, Laumanns M, Bleuler S (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195

    Article  Google Scholar 

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Authors and Affiliations

  1. CFD+engineering, IB Fischer CFD+engineering GmbH, Lipowskystr. 12, 81373, Munich, Germany

    B. Fabritius

  2. CEMPS, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, UK

    G. Tabor

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  1. B. Fabritius
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  2. G. Tabor
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Correspondence to G. Tabor.

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Fabritius, B., Tabor, G. Improving the quality of finite volume meshes through genetic optimisation. Engineering with Computers 32, 425–440 (2016). https://doi.org/10.1007/s00366-015-0423-0

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