Skip to main content
Log in

Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper presents a set of parallel procedures for anisotropic mesh adaptation accounting for mixed element types used in boundary layer meshes, i.e., the current procedures operate in parallel on distributed boundary layer meshes. The procedures accept anisotropic mesh metric field as an input for the desired mesh size field and apply local mesh modifications to adapt the mesh to match/satisfy the specified mesh size field. The procedures fully account for the parametric geometry of curved domains and maintain the semi-structured nature of the boundary layer elements. The effectiveness of the procedures is demonstrated on three viscous flow examples that include the ONERA M6 wing, a heat transfer manifold, and a scramjet engine.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33

Similar content being viewed by others

References

  1. Gropp W, Lusk E, Skjellum A (2014) Using MPI: portable parallel programming with the message-passing interface. MIT Press, Cambridge. https://mitpress.mit.edu/using-MPI-3ed

  2. Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, New York

    Book  MATH  Google Scholar 

  3. Alauzet F, Li X, Seol ES, Shephard MS (2006) Parallel anisotropic 3D mesh adaptation by mesh modification. Eng Comput 21(3):247–258. doi:10.1007/s00366-005-0009-3

    Article  Google Scholar 

  4. Au P, Dompierre J, Labbe P, Guibault F, Camarero R (1998) Proposal of benchmarks for 3D unstructured tetrahedral mesh optimization. In: Proceedings of the 7th International Meshing Roundtable, pp 459–478

  5. Bänsch E (1991) Local mesh refinement in 2 and 3 dimensions. IMPACT Comput Sci Eng 3(3):181–191

    Article  MathSciNet  MATH  Google Scholar 

  6. Becker R, Rannacher R (2001) An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer 10(1):1–102

    MathSciNet  MATH  Google Scholar 

  7. Botasso CL (2004) Anisotropic mesh adaption by metric-driven optimization. Int J Numer Methods Eng 60(3):597–639. doi:10.1002/nme.977

    Article  MathSciNet  MATH  Google Scholar 

  8. Bottasso CL, Detomi D (2002) A procedure for tetrahedral boundary layer mesh generation. Eng Comput 18(1):66–79. doi:10.1007/s003660200006

    Article  MATH  Google Scholar 

  9. Bourgault Y, Picasso M, Alauzet F, Loseille A (2009) On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows. Int J Numer Methods Fluids 59(1):47–74. doi:10.1002/fld.1797

    Article  MathSciNet  MATH  Google Scholar 

  10. Buscaglia GC, Dari EA (1997) Anisotropic mesh optimization and its application in adaptivity. Int J Numer Methods Eng 40:4119–4136

    Article  MATH  Google Scholar 

  11. Castro-Diáz MJ, Hecht F, Mohammadi B, Pironneau O (1997) Anisotropic unstructured mesh adaption for flow simulations. Int J Numer Methods Fluids 25:475–491

    Article  MathSciNet  MATH  Google Scholar 

  12. Chand KK, Diachin LF, Li X, Ollivier-Gooch C, Seol ES, Shephard MS, Tautges T, Trease H (2008) Toward interoperable mesh, geometry and field components for pde simulation development. Eng Comput 24(2):165–182. doi:10.1007/s00366-007-0080-z

    Article  Google Scholar 

  13. Chandra S, Li X, Saif T, Parashar M (2007) Enabling scalable parallel implementations of structured adaptive mesh refinement applications. J Supercomput 39(2):177–203. doi:10.1007/s11227-007-0110-z

    Article  Google Scholar 

  14. Chitale K, Sahni O, Tendulkar S, Nastasia R, Shephard M, Jansen K (2013) Boundary layer adaptivity for transonic turbulent flows. AIAA Paper 13-2445. doi:10.2514/6.2013-2445

  15. Connell SD, Braaten ME (1995) Semistructured mesh generation for three-dimensional Navier–Stokes calculations. AIAA J 33(6):1017–1024

    Article  MATH  Google Scholar 

  16. de Cougny HL, Shephard MS (1999) Parallel refinement and coarsening of tetrahedral meshes. Comput Methods Appl Mech Eng 46:1101–1125

    MathSciNet  MATH  Google Scholar 

  17. de Cougny HL, Shephard MS, Georges MK (1990) Explicit node point mesh smoothing within the octree mesh generator. Tech. Rep. 1990-10, Rensselaer Polytechnic Institute, Troy

  18. Cray: Cray XE6. [Online]. http://www.cray.com/Products/XE/CrayXE6System.aspx. Accessed 19 Sep 2012

  19. Foster TM, Mohamed MS, Trevelyan J, Coates G (2012) Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis. Eng Anal Bound Elem 36(9):1331–1343. doi:10.1016/j.enganabound.2012.02.020

    Article  MathSciNet  MATH  Google Scholar 

  20. Freitag LA, Ollivier-Gooch C (1997) Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Methods Eng 40(21):3979–4002

    Article  MathSciNet  MATH  Google Scholar 

  21. Frey PJ, Alauzet F (2005) Anisotropic mesh adaptation for CFD computations. Comput Methods Appl Mech Eng 194(48–49):5068–5082. doi:10.1016/j.cma.2004.11.025

    Article  MathSciNet  MATH  Google Scholar 

  22. Garimella RV, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations. Int J Numer Methods Eng 49:193–218

    Article  MATH  Google Scholar 

  23. George P, Borouchaki H, Laug P (2002) An efficient algorithm for 3D adaptive meshing. Adv Eng Softw 33(7):377–387

    Article  MATH  Google Scholar 

  24. Giles MB, Süli E (2002) Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numer 11(1):145–236

    MathSciNet  MATH  Google Scholar 

  25. Hassan O, Morgan K, Probert EJ, Peraire J (1996) Unstructured tetrahedral mesh generation for three-dimensional viscous flows. Int J Numer Methods Eng 39:549–567

    Article  MATH  Google Scholar 

  26. Hassan O, Morgan K, Weatherill N (2007) Unstructured mesh methods for the solution of the unsteady compressible flow equations with moving boundary components. Philos Trans R S A Math Phys Eng Sci 365(1859):2531–2552

    Article  MathSciNet  Google Scholar 

  27. Ito Y, Murayama M, Yamamoto K, Shih AM, Soni BK (2013) Efficient hybrid surface/volume mesh generation using suppressed marching-direction method. AIAA J 51(6):1450–1461

    Article  Google Scholar 

  28. Ito Y, Nakahashi K (2002) Unstructured mesh generation for viscous flow computations. In: Proceedings of the 11th International Meshing Roundtable, pp 367–377

  29. Joe B (1995) Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J Sci Comput 16(6):1292–1307

    Article  MathSciNet  MATH  Google Scholar 

  30. Kallinderis Y, Kavouklis C (2005) A dynamic adaptation scheme for general 3-D hybrid meshes. Comput Methods Appl Mech Eng 194(48–49):5019–5050. doi:10.1016/j.cma.2004.11.023

    Article  MATH  Google Scholar 

  31. Kallinderis Y, Vijayan P (1993) Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes. AIAA J 31(8):1440–1447

    Article  Google Scholar 

  32. Kavouklis C, Kallinderis Y (2010) Parallel adaptation of general three-dimensional hybrid meshes. J Comput Phys 229(9):3454–3473. doi:10.1016/j.jcp.2010.01.011

    Article  MathSciNet  MATH  Google Scholar 

  33. Khawaja A, Kallinderis Y (2000) Hybrid grid generation for turbomachinery and aerospace applications. Int J Numer Methods Eng 49(1–2):145–166

    Article  MATH  Google Scholar 

  34. Khawaja A, Minyard T, Kallinderis Y (2000) Adaptive hybrid grid methods. Comput Methods Appl Mech Eng 189(4):1231–1245. doi:10.1016/S0045-7825(99)00375-8

    Article  MATH  Google Scholar 

  35. Li X (2003) Mesh modification procedures for general 3D non-manifold domains. Ph.D. Dissertation, Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy

  36. Li X, Remacle JF, Chevaugeon N, Shephard MS (2004) Anisotropic mesh gradation control. In: Proceedings of the 13th International Meshing Roundtable, pp 401–412

  37. Li X, Shephard M, Beall M (2005) 3D anisotropic mesh adaptation by mesh modifications. Comput Methods Appl Mech Eng 194(48–49):4915–4950. doi:10.1016/j.cma.2004.11.019

    Article  MathSciNet  MATH  Google Scholar 

  38. Li X, Shephard MS, Beall MW (2003) Accounting for curved domains in mesh adaptation. Int J Numer Methods Eng 58(2):247–276. doi:10.1002/nme.772

    Article  MATH  Google Scholar 

  39. Liu A, Joe B (1994) On the shape of tetrahedra from bisection. Math Comput 63(207):141–154

    Article  MathSciNet  MATH  Google Scholar 

  40. Löhner R, Baum JD (1992) Adaptive h-refinement on 3D unstructured grids for transient problems. Int J Numer Methods Fluids 14(12):1407–1419

    Article  MATH  Google Scholar 

  41. Lohner R, Cebral J (2000) Generation of non-isotropic unstructured grids via directional enrichment. Int J Numer Methods Eng 49(1–2):219–232

    Article  MATH  Google Scholar 

  42. Loseille A, Löhner R (2013) Robust boundary layer mesh generation. In: Proceedings of the 21st International Meshing Roundtable, pp 493–511

  43. Marcum DL (1995) Generation of unstructured grids for viscous flow applications. AIAA Paper 95-0212

  44. Muller J, Sahni O, Li X, Jansen KE, Shephard MS, Taylor CA (2005) Anisotropic adaptive finite element method for modeling blood flow. Comput Methods Biomech Biomed Eng 8(5):295–305. doi:10.1080/10255840500264742

    Article  Google Scholar 

  45. NASA: CIAM Axisymmetric Scramjet. [Online]. http://hapb-www.larc.nasa.gov/Public/Engines/Ciam/Ciam.html. Accessed 19 Sep 2012

  46. NASA: FUN3D online manual. [Online]. http://fun3d.larc.nasa.gov/. Accessed 19 Sep 2012

  47. Oliker L, Biswas R, Gabow HN (2000) Parallel tetrahedral mesh adaptation with dynamic load balancing. Parallel Comput 26(12):1583–1608

    Article  MATH  Google Scholar 

  48. Ovcharenko A, Ibanez D, Delalondre F, Sahni O, Jansen KE, Carothers CD, Shephard MS (2012) Neighborhood communication paradigm to increase scalability in large-scale dynamic scientific applications. Parallel Comput 38(3):140–156. doi:10.1016/j.parco.2011.10.013

    Article  Google Scholar 

  49. Pain CC, Umpleby AP, de Oliveira CRE, Goddard AJH (2001) Tetrahedral mesh optimization and adaptivity for steady-state and transient finite element calculations. Comput Methods Appl Mech Eng 190(29–30):3771–3796. doi:10.1016/S0045-7825(00)00294-2

    Article  MATH  Google Scholar 

  50. Park YM, Kwon OJ (2005) A parallel unstructured dynamic mesh adaptation algorithm for 3-D unsteady flows. Int J Numer Methods Fluids 48(6):671–690

    Article  MATH  Google Scholar 

  51. Peraire J, Peiro J, Morgan K (1992) Adaptive remeshing for three-dimensional compressible flow computation. J Comput Phys 103(2):269–285. doi:10.1016/0021-9991(92)90401-J

    Article  MATH  Google Scholar 

  52. Pirzadeh S (1994) Unstructured viscous grid generation by the advancing-layers method. AIAA J 32(8):1735–1737

    Article  Google Scholar 

  53. Sahni O, Jansen KE, Shephard MS, Taylor CA, Beall MW (2008) Adaptive boundary layer meshing for viscous flow simulations. Eng Comput 24(3):267–285. doi:10.1007/s00366-008-0095-0

    Article  Google Scholar 

  54. Sahni O, Muller J, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comput Methods Appl Mech Eng 195(41–43):5634–5655. doi:10.1016/j.cma.2005.10.018

    Article  MathSciNet  MATH  Google Scholar 

  55. Sahni O, Zhou M, Shephard MS, Jansen KE (2009) Scalable implicit finite element solver for massively parallel processing with demonstration to 160K cores. In: Proceedigs of the 2009 ACM/IEEE Conference on High Performance Computing

  56. Sandia National Laboratories: Zoltan unstructured communication utilities. [Online]. http://www.cs.sandia.gov/Zoltan/ug_html/ug_util_comm.html. Accessed 19 Sep 2012

  57. Seol ES, Shephard MS (2006) Efficient distributed mesh data structure for parallel automated adaptive analysis. Eng Comput 22(3–4):197–213

    Article  Google Scholar 

  58. Shephard MS, Beall MW, O’Bara RM, Webster BE (2004) Toward simulation-based design. Finite Elem Anal Design 40(12):1575–1598. doi:10.1016/j.finel.2003.11.004

    Article  Google Scholar 

  59. Stogner RH, Carey GF, Murray BT (2008) Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements. Int J Numer Methods Eng 76(5):636–661. doi:10.1002/nme.2337

    Article  MATH  Google Scholar 

  60. Toussaint GT, Verbrugge C, Wang C, Zhu B (1993) Tetrahedralization of simple and non-simple polyhedra. In: Proceedings of the 5th Canadian Conference on Computational Geometry, pp 24–29

  61. Schmitt V, Charpin F (1979) Pressure distribution on the ONERA-M6-Wing at transonic mach numbers. In: Report of the Fluid Dynamics Panel Working Group 04, vol 138. AGARD

  62. Verfürth R (1996) A review of posteriori error estimation and adaptive mesh-refinement techniques. Teubner-Wiley, Stuttgart

    MATH  Google Scholar 

  63. Whiting CH, Jansen KE (2001) A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int J Numer Methods Fluids 35(1):93–116

    Article  MATH  Google Scholar 

  64. Xie T, Seol ES, Shephard MS (2012) Generic components for petascale automated adaptive simulations. Eng Comput (Accepted for publication)

  65. Zhang L, Chang X, Duan X, Zhao Z, He X (2012) Applications of dynamic hybrid grid method for three-dimensional moving/deforming boundary problems. Comput Fluids 62:45–63. doi:10.1016/j.compfluid.2012.03.008

    Article  MathSciNet  MATH  Google Scholar 

  66. Zhou M, Sahni O, Kim HJ, Figueroa CA, Taylor CA, Shephard MS, Jansen KE (2010) Cardiovascular flow simulation at extreme scale. Comput Mechan 46(1):71–82. doi:10.1007/s00466-009-0450-z

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Science Foundation under Grant No. 0749152, and by the U.S. Department of Energy under DOE Grant No. DE-FC02-06ER25769, and by the NASA STTR Part II Grant No. BEE103/NNX11CC69C. Computing support is provided by the National Energy Research Scientific Computing Center for granting access to the Hopper Cray XE6 supercomputer. Resources at the Center for Computational Innovations (CCI) at Rensselaer were also used for testing and development. The authors would like to acknowledge the help of Dr. L. Fovargue on the ONERA M6 case and F. Nihan Cayan and O. Breslouer for help with the scramjet case.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Onkar Sahni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahni, O., Ovcharenko, A., Chitale, K.C. et al. Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations. Engineering with Computers 33, 767–795 (2017). https://doi.org/10.1007/s00366-016-0437-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-016-0437-2

Keywords

Navigation