Skip to main content
SpringerLink
Log in

Finite element mesh generation for subsurface simulation models

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

Abstract

This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in gOcad software. Subsurface simulation models have an intrinsic heterogeneous characteristic due to the different geomechanics properties of each geological layer. This type of modeling should represent geometry of natural objects, such as geological horizons and faults, which have faceted representations. In addition, in subsurface simulation modeling, lower-dimension degenerated parts, such as dangling surfaces, should be represented. These requirements pose complex modeling problems, which, in general, are not treated by a generic geometric modeler. Therefore, this paper describes four important modeling capabilities that are implemented in a subsurface simulation modeler: surface re-triangulation, surface intersection, automatic volume recognition, and tetrahedral mesh generation. Surface re-triangulation is used for regenerating the underlying geometric support of surfaces imported from gOcad and of surface patches resulting from intersection. The same re-triangulation algorithm is used for generating FE surface meshes. The proposed modeling methodology combines, with some adaptation, meshing algorithms previously published by the authors. Two novel techniques are presented, the first for surface intersection and the second for automatic volume recognition. The main contribution of the present work is the integration of such techniques through a methodology for the solution of mesh generation problems in subsurface simulation modeling. An example illustrates the capabilities of the proposed methodology. Shape quality of generated triangular surface and tetrahedral meshes, as well as the efficiency of the 3D mesh generator, is demonstrated by means of this example.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Gocad (2006) gOcad Publications. http://www.gocad.org/w4/index.php/research/publications

  2. Mallet JL (1997) Discrete modeling for natural objects. Math Geol 29(2):199–219

    Article  MATH  MathSciNet  Google Scholar 

  3. Gemmer L, Huuse M, Clausen OR, Nielsen SB (2002) Mid-Paleocene palaeogeography of the eastern North Sea basin: integrating geological evidence and 3D geodynamic modelling. Basin Res 14:329–346

    Article  Google Scholar 

  4. Wu Q, Xu H (2003) An approach to computer modeling and visualization of geological faults in 3D. Comput Geosci 29:503–509

    Article  Google Scholar 

  5. Wu Q, Xu H (2001) A framework modeling of geological related spatial data in 3D scene. In: Sixth international symposium on future software technology, Zhengzhou, China, pp 252–257

  6. Martelet G, Calcagno P, Gumiaux C, Truffert C, Bitri A, Gapais D, Brun JP (2004) Integrated 3D geophysical and geological modelling of the Hercynian Suture Zone in the Champtoceaux area (south Brittany, France). Tectonophysics 382:117–128

    Article  Google Scholar 

  7. Lixin W (2004) Topological relations embodied in a generalized tri-prism (GTP) model for a 3D geoscience modeling system. Comput Geosci 30:405–418

    Article  Google Scholar 

  8. Wu Q, Xu H, Zou X (2005) An effective method for 3D geological modeling with multi-source data integration. Comput Geosci 31:35–43

    Article  MATH  Google Scholar 

  9. Qu H, Pan M, Wang Z, Wang B, Chai H, Xue S (2005)A new method for 3D geological reconstruction from intersected cross-sections. In: International symposium of remote sensing and space technology for multidiciplinary research and application

  10. Butscher C, Huggenberger P (2007) Implications for karst hydrology from 3D geological modeling using the aquifer base gradient approach. J Hydrol 342:184–198

    Article  Google Scholar 

  11. Kaufmann O, Martin T (2008) 3D geological modelling from boreholes, cross-sections and geological maps, application over former natural gas storages in coal mines. Comput Geosci 34:278–290

    Article  Google Scholar 

  12. Zanchi A, Francesca S, Stefanoa Z, Simone S, Graziano G (2009) 3D reconstruction of complex geological bodies: examples from the Alps. Comput Geosci 35:49–69

    Article  Google Scholar 

  13. Ming J, MaoPan QuH, Ge Z (2010) GSIS: a 3D geological multi body modeling system from netty cross-sections with topology. Comput Geosci 36:756–767

    Article  Google Scholar 

  14. Xu N, Tian H, Kulatilake PHSW, Duan Q (2011) Building a three dimensional sealed geological model to use in numerical stress analysis software: a case study for a dam site. Comput Geotech 38:1022–1030

    Article  Google Scholar 

  15. Miranda ACO, Martha LF, Wawrzynek PA, Ingraffea AR (2009) Surface mesh regeneration considering curvatures. Eng Comput 25(2):207–219. doi:10.1007/s00366-008-0119-9

    Article  Google Scholar 

  16. Cavalcante-Neto JB, Wawrzynek PA, Carvalho MTM, Martha LF, Ingraffea AR (2001) An algorithm for three-dimensional mesh generation for arbitrary regions with cracks. Eng Comput 17(1):75–91

    Article  MATH  Google Scholar 

  17. Baumgart BG (1975) A polyhedron representation for computer vision. AFISPS 44:589–596

    Google Scholar 

  18. Mäntylä M (1988) An introduction to solid modeling. Computer Science Press, Rockville

    Google Scholar 

  19. Weiler KJ (1986) Topological structures for geometric modeling. PhD thesis, Rensselaer Polytechnic Institute, Troy, New York

  20. de Berg M, Cheong O, van Kreveld M, Overmars M (2008) Computational geometry–algorithms and applications. Springer, Berlin

    MATH  Google Scholar 

  21. Lohner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing-front method. Int J Numer Methods Fluids 8:1135–1149

    Article  Google Scholar 

  22. Peraire J, Peiro J, Formaggia L, Morgan K, Zienkiewicz OC (1988) Finite Euler computation in three-dimensions. Int J Numer Methods Eng 26:2135–2159

    Article  MATH  Google Scholar 

  23. Jin H, Tanner RI (1993) Generation of unstructured tetrahedral meshes by advancing front technique. Int J Numer Methods Eng 36(11):1805–1823

    Article  MATH  Google Scholar 

  24. Moller P, Hansbo P (1995) On advancing front mesh generation in three dimensions. Int J Numer Methods Eng 38(21):3551–3569

    Article  MathSciNet  Google Scholar 

  25. Chan CT, Anastasiou K (1997) Automatic tetrahedral mesh generation scheme by the advancing front method. Commun Numer Methods Eng 13(1):33–46

    Article  MATH  MathSciNet  Google Scholar 

  26. Rassineux A (1998) Generation and optimization of tetrahedral meshes by advancing front technique. Int J Numer Methods Eng 41(4):651–674

    Article  MATH  Google Scholar 

  27. Miranda ACO, Lira WWM, Cavalcante-Neto JB, Sousa RA, Martha LF (2013) A 3D adaptive mesh generation approach using geometric modeling with multi-regions and parametric surfaces. J Comput Inf Sci Eng 13(2):021002-1–021002-13. doi:10.1115/1.4024106

    Article  Google Scholar 

  28. Foley TA, Nielson GM (1989) Knot selection for parametric spline interpolation. In: Mathematical methods in computer aided geometric design. Academic Press Professional, Inc., pp 261–272

  29. Meagher D (1980) Octree Encoding: a new technique for the representation, manipulation and display of arbitrary 3-D objects, Computer. Rensselaer Polytechnic Institute

  30. Guttman A (1984) R trees: a dynamic index structure for spatial searching. In: ACM SIGMOD international conference on management of data, pp 47–57

  31. Rudolf B (1971) Binary B-trees for virtual memory. In: ACM-SIGFIDET workshop, San Diego, California, pp 219–235

  32. Löhner R (1996) Regridding surface triangulations. J Comput Phys 126 (1):1–10. doi:http://dx.doi.org/10.1006/jcph.1996.0115

    Google Scholar 

  33. Schreiner J, Scheidegger CE, Fleishman S, Silva CT (2006) Direct (Re)meshing for efficient surface processing. Comput Graph Forum 25(3):527–536. doi:10.1111/j.1467-8659.2006.00972.x

    Article  Google Scholar 

  34. Lo SH (1995) Automatic mesh generator over intersecting surfaces. Int J Numer Methods Eng 38:943–954

    Article  MATH  Google Scholar 

  35. Segura RJ, Feito FR (1998) An algorithm for determining intersection segment-polygon in 3D. Comput Graph 22(5):587–592

    Article  Google Scholar 

  36. Jiménez JJ, Segura RJ, Feito FR (2009) A robust segment-triangle intersection algorithm for interference tests. Comput Geom 43(5):474–492

    Article  Google Scholar 

  37. Shewchuk JR (1996) Robust adaptive floating-point geometric predicates. In: Twelfth annual symposium on computational geometry, pp 141–150

  38. Shewchuk JR (1997) Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discret Comput Geom 18:305–363

    Article  MATH  MathSciNet  Google Scholar 

  39. Preparata FP, Shamos MI (1990) Computational geometry: an introduction. Springer Verlag, New York

    Google Scholar 

  40. Miranda ACO, Cavalcante-Neto JB, Martha LF (1999) An algorithm for two-dimensional mesh generation for arbitrary regions with cracks. XII Brazilian symposium on computer graphics and image processing (Cat NoPR00481):29–38

  41. Cavalcante-Neto JB, Martha LF, Wawrzynek PA, Ingraffea AR (2005) A back-tracking procedure for optimization of simplex meshes. Commun Numer Methods Eng 21(12):711–722

    Article  MATH  MathSciNet  Google Scholar 

  42. Coelho LC (2006) MG-mesh generator, www.tecgraf.puc-rio.br/~lula/manual/mg.pdf. Tecgraf, Rio de Janeiro

  43. Taubin G (1995) Curve and surface smoothing without shrinkage. In: Fifth international conference on computer vision, pp 852–857

  44. Cavalcanti PR, Carvalho PCP, Martha LF (1997) Non-manifold modeling: an approach based on spatial subdivision. Comput Aided Des 29(3):209–220

    Article  Google Scholar 

  45. Krysl P (1996) Computational complexity of the advancing front triangulation. Eng Comput 12:16–22

    Article  Google Scholar 

  46. Bonet J, Peraire J (1991) An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems. Int J Numer Methods Eng 31(1):1–17

    Article  MATH  MathSciNet  Google Scholar 

  47. Gosselin S, Ollivier-Gooch C (2011) Tetrahedral mesh generation using delaunay refinement with non-standard quality measures. Int J Numer Methods Eng 87:795–820

    Article  MATH  MathSciNet  Google Scholar 

  48. Klingner BM, Shewchuk (2007) Aggressive tetrahedral mesh improvement. In: 16th international meshing roundtable, pp 2–23

  49. Alliez P, Cohen-Steiner D, Yvinec M, Desbrun M (2005) Variational tetrahedral meshing. ACM Trans Graph 24(3):617–625

    Article  Google Scholar 

  50. Miranda ACO, Martha LF (2002) Mesh generation on high-curvature surfaces based on a background quadtree structure. In: proceedings of 11th international meshing roundtable 1:333–341

  51. Knupp PM (2001) Algebraic mesh quality metrics. SIAM J Sci Comput 23(1):193–218

    Article  MATH  MathSciNet  Google Scholar 

  52. Canann SA, Tristano JR, Staten ML (1998) An approach to combined laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes. In: 7th international mesh roundtable, pp 479–494

Download references

Acknowledgments

The authors would like to thank the National Council for Scientific and Technological Development (CNPq), University of Brasília, the Technical-Scientific Software Development Institute (Tecgraf/PUC-Rio), and Pontifical Catholic University of Rio de Janeiro (PUC-Rio) for the financial support and for providing the necessary space and resources used during the development of this work.

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Brasília, SG-12 Building, Darcy Ribeiro Campus, Brasilia, DF, 70910-900, Brazil

    Antonio Carlos de Oliveira Miranda

  2. Laboratory of Scientific Computing and Visualization-LCCV, Technology Center, Federal University of Alagoas, Maceio, AL, 57072-970, Brazil

    William Wagner Matos Lira

  3. Department of Civil Engineering and Tecgraf - Technical-Scientific Software Development Institute, Pontifical Catholic University of Rio de Janeiro, Rua Marques de São Vicente 225, Rio de Janeiro, 22451-900, Brazil

    Ricardo Cavalcanti Marques & Luiz Fernando Martha

  4. Engineering School, Fluminense Federal University, Rua Passo da Patria 156, Niterói, 24210-240, Brazil

    Andre Maues Brabo Pereira

  5. Department of Computing, Federal University of Ceará, Campus do Pici, Bloco 910, Fortaleza, 60455-760, Brazil

    Joaquim B. Cavalcante-Neto

Authors
  1. Antonio Carlos de Oliveira Miranda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Wagner Matos Lira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ricardo Cavalcanti Marques
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andre Maues Brabo Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Joaquim B. Cavalcante-Neto
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Luiz Fernando Martha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Carlos de Oliveira Miranda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Oliveira Miranda, A.C., Lira, W.W.M., Marques, R.C. et al. Finite element mesh generation for subsurface simulation models. Engineering with Computers 31, 305–324 (2015). https://doi.org/10.1007/s00366-014-0352-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-014-0352-3

Keywords

Search

Navigation