The Impact of the Mesh Partitioning Factors on CFD Simulation

  • Chen Cui
  • Juan Chen
  • Feihao Wu
  • Miao Wang
  • Yuyang Sun
  • Xinhai Xu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 768)


Mesh partitioning plays an important role in Computational Fluid Dynamics (CFD) simulation. However, it is difficult to produce a good mesh partitioning to achieve a high performance simulation because it is a NP-complete problem to solve this problem. A good mesh partitioning may be determined by many factors. Nowadays, there is a lack of systematic guidelines and comprehensive analyses for how to produce a high quality mesh partitioning. Considering that it is difficult to break through in theory, we prefer to explore how the factors related to mesh partitioning influence CFD simulation based on a large amount of experimental analyses. In this paper, we evaluate the impact of changing the mesh partitioning factors on mesh partitioning quality and simulation performance according to the following five factors: the number of processor faces, subdomain aspect ratio, load, partitioning direction and mapping. We design a series of rules to make various and numerous mesh partitioning changes based on four commonly used methods (Simple, Metis, Scotch and Manual) in OpenFOAM. Furthermore, we conduct the parallel simulation for two representative cases (cavity case and damBreak case) in OpenFOAM framework. The experimental results certify that changing mesh partitioning factors really influences the simulation performance. Then we provide some analyses and advices, which will definitely be helpful to guide mesh partitioning in the future.


Mesh partitioning CFD simulation Mesh partitioning quality Simulation performance 



The authors would like to thank to the funding from the National Natural Science Foundation of China under grant No.61221491, No.61303071, No.61303068, No.61303063, No.61303061 and No.61120106005, and Open Fund (No. 201402-01, No.201503-01 and No.201503-02) from State Key Laboratory of High Performance Computing.


  1. 1.
    Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. Army High Performance Computing Research Center (2000)Google Scholar
  2. 2.
    Walshaw, C., Cross, M.: Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM J. Sci. Comput. 22(1), 63–80 (2000)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Berger, M.J., Bokhari, S.H.: A partitioning strategy for nonuniform problems on multiprocessors. IEEE Trans. Comput. 36(5), 570–580 (1987)CrossRefGoogle Scholar
  4. 4.
    Aftosmis, M., Berger, M., Murman, S.: Applications of space-filling-curves to cartesian methods for CFD. In: 42nd AIAA Aerospace Sciences Meeting and Exhibit, p. 1232 (2004)Google Scholar
  5. 5.
    Simon, H.D.: Partitioning of unstructured problems for parallel processing. Comput. Syst. Eng. 2(2–3), 135–148 (1991)CrossRefGoogle Scholar
  6. 6.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Diekmann, R., Preis, R., Schlimbach, F., Walshaw, C.: Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM. Parallel Comput. 26(12), 1555–1581 (2000)CrossRefMATHGoogle Scholar
  8. 8.
    Vanderstraeten, D., Keunings, R.: Beyond conventional mesh partitioning algorithms and the minimum edge cut criterion: Impact on realistic applications. Technical report. Society for Industrial and Applied Mathematics, Philadelphia, PA (United States) (1995)Google Scholar
  9. 9.
    Farhat, C., Maman, N., Brown, G.W.: Mesh partitioning for implicit computations via iterative domain decomposition: impact and optimization of the subdomain aspect ratio. Int. J. Numer. Methods Eng. 38(6), 989–1000 (1995)CrossRefMATHGoogle Scholar
  10. 10.
    Li, H., Xu, X., Tang, Y., et al.: A multi-user performance analysis framework for CFD simulations. Prog. Comput. Fluid Dyn. Int. J. 17(4), 199–211 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bhatelé, A., Kalé, L.V., Kumar, S.: Dynamic topology aware load balancing algorithms for molecular dynamics applications. In: Proceedings of the 23rd International Conference on Supercomputing, pp. 110–116. ACM (2009)Google Scholar
  12. 12.
    Aktulga, H.M., Yang, C., Ng, E.G., Maris, P., Vary, J.P.: Topology-aware mappings for large-scale eigenvalue problems. In: Kaklamanis, C., Papatheodorou, T., Spirakis, P.G. (eds.) Euro-Par 2012. LNCS, vol. 7484, pp. 830–842. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32820-6_82 CrossRefGoogle Scholar
  13. 13.
    Karypis, G., Kumar, V.: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Department of Computer Science and Engineering, Army HPC Research Center, University of Minnesota, Minneapolis, MN (1998)Google Scholar
  14. 14.
    Pellegrini, F., Roman, J.: Scotch: a software package for static mapping by dual recursive bipartitioning of process and architecture graphs. In: Liddell, H., Colbrook, A., Hertzberger, B., Sloot, P. (eds.) HPCN-Europe 1996. LNCS, vol. 1067, pp. 493–498. Springer, Heidelberg (1996). doi: 10.1007/3-540-61142-8_588 CrossRefGoogle Scholar
  15. 15.
    Walshaw, C., Cross, M.: JOSTLE: parallel multilevel graph-partitioning software – an overview. In: Magoules, F. (ed.) Mesh Partitioning Techniques and Domain Decomposition Techniques, pp. 27–58. Civil-Comp Ltd. (2007)Google Scholar
  16. 16.
    Devine, K., Boman, E., Heaphy, R., Hendrickson, B., Vaughan, C.: Zoltan data management service for parallel dynamic applications. Comput. Sci. Eng. 4(2), 90–97 (2002)CrossRefGoogle Scholar
  17. 17.
    Shang, Z.: Large-scale CFD parallel computing dealing with massive mesh. J. Eng. 2013, 6 (2013). Article ID 850148CrossRefGoogle Scholar
  18. 18.
    Šidlof, P., Horáček, J., Řidkỳ, V.: Parallel CFD simulation of flow in a 3D model of vibrating human vocal folds. Comput. Fluids 80, 290–300 (2013)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Wang, M., Tang, Y., Guo, X., Ren, X.: Performance analysis of the graph-partitioning algorithms used in OpenFOAM. In: 2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI), pp. 99–104. IEEE (2012)Google Scholar
  20. 20.
    Walshaw, C., Cross, M., Diekmann, R., Schlimbach, F.: Multilevel mesh partitioning for optimising aspect ratio. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds.) VECPAR 1998. LNCS, vol. 1573, pp. 285–300. Springer, Heidelberg (1999). doi: 10.1007/10703040_23 CrossRefGoogle Scholar
  21. 21.
    Rao, A.R.M.: Parallel mesh-partitioning algorithms for generating shape optimised partitions using evolutionary computing. Adv. Eng. Softw. 40(2), 141–157 (2009)CrossRefMATHGoogle Scholar
  22. 22.
    OpenFOAM User Guide: Version 2.3.0, 5 February 2014Google Scholar
  23. 23.
    Guo, X.W., Zou, S., Yang, X., Yuan, X.F., Wang, M.: Interface instabilities and chaotic rheological responses in binary polymer mixtures under shear flow. RSC Adv. 4(105), 61167–61177 (2014)CrossRefGoogle Scholar
  24. 24.
    Zhang, T.T., Yang, W.J., Lin, Y.F., Cao, Y., Wang, M., Wang, Q., Wei, Y.X.: Numerical study on flow rate limitation of open capillary channel flow through a wedge. Adv. Mech. Eng. 8(4), 1–11 (2016). doi: 10.1177/1687814016645487 Google Scholar
  25. 25.
    Li, C., Yang, W., Xu, X., Wang, J., Wang, M., Xu, L.: Numerical investigation of fish exploiting vortices based on the kármán gaiting model. Ocean Eng. 140, 7–18 (2017)CrossRefGoogle Scholar
  26. 26.
    Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring. I. Math. Comput. 47(175), 103–134 (1986)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring. II. Math. Comput. 49(179), 1–16 (1987)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Chen Cui
    • 1
  • Juan Chen
    • 1
  • Feihao Wu
    • 1
  • Miao Wang
    • 1
  • Yuyang Sun
    • 2
  • Xinhai Xu
    • 1
  1. 1.State Key Laboratory of High Performance Computing, College of ComputerNational University of Defense TechnologyChangshaChina
  2. 2.College of ComputerNational University of Defense TechnologyChangshaChina

Personalised recommendations