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Multiscale mesh generation on the sphere

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Abstract

A method for generating computational meshes for applications in ocean modeling is presented. The method uses a standard engineering approach for describing the geometry of the domain that requires meshing. The underlying sphere is parametrized using stereographic coordinates. Then, coastlines are described with cubic splines drawn in the stereographic parametric space. The mesh generation algorithm builds the mesh in the parametric plane using available techniques. The method enables to import coastlines from different data sets and, consequently, to build meshes of domains with highly variable length scales. The results include meshes together with numerical simulations of various kinds.

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Notes

  1. TIMOTHY, Tracing and Integrated Modeling of Natural and Anthropogenic Effects on Hydrosystems: The Scheldt River basin and adjacent coastal North Sea, http://www.climate.be/TIMOTHY.

  2. SLIM, Second-generation Louvain-la-Neuve Ice-ocean Model, http://www.climate.be/SLIM

References

  • Arya S, Mount DM, Netanyahu NS, Silverman R, Wu AY (1998) An optimal algorithm for approximate nearest neighbor searching. J ACM 45:891–923. http://www.cs.umd.edu/ mount/ANN/

    Article  Google Scholar 

  • Beall MW, Shephard MS (1997) A general topology-based mesh data structure. Int J Numer Methods Eng 40(9):1573–1596

    Article  Google Scholar 

  • Danilov S, Kivman G, Schröter J (2005) Evaluation of an eddy-permitting finite-element ocean model in the north atlantic. Ocean Model 10:35–49

    Article  Google Scholar 

  • Dwyer RA (1986) A simple divide-and-conquer algorithm for computing delaunay triangulations in o(n log log n) expected time. In: Proceedings of the second annual symposium on computational geometry, Yorktown Heights, 2–4 June 1986, pp 276–284

  • George P-L, Frey P (2000) Mesh generation. Hermes, Lyon

    Google Scholar 

  • Gorman G, Piggott M, Pain C (2007) Shoreline approximation for unstructured mesh generation. Comput Geosci 33:666–677

    Article  Google Scholar 

  • Gorman G, Piggott M, Pain C, de Oliveira R, Umpleby A, Goddard A (2006) Optimisation based bathymetry approximation through constrained unstructured mesh adaptivity. Ocean Model 12:436–452

    Article  Google Scholar 

  • Griffies SM, Böning C, Bryan FO, Chassignet EP, Gerdes R, Hasumi H, Hirst A, Treguier A-M, Webb D (2000) Developments in ocean climate modeling. Ocean Model 2:123–192

    Article  Google Scholar 

  • Hagen SC, Westerink JJ, Kolar RL, Horstmann O (2001) Two-dimensional, unstructured mesh generation for tidal models. Int J Numer Methods Fluids 35:669–686 (printed version in Richard’s office)

    Article  Google Scholar 

  • Haimes R (2000) CAPRI: computational analysis programming interface (a solid modeling based infra-structure for engineering analysis and design). Tech. rep., Massachusetts Institute of Technology

  • Henry RF, Walters RA (1993) Geometrically based, automatic generator for irregular triangular networks. Commun Numer Methods Eng 9:555–566

    Article  Google Scholar 

  • Lambrechts J, Hanert E, Deleersnijder E, Bernard P-E, Legat V, Wolanski J-FRE (2008) A high-resolution model of the whole great barrier reef hydrodynamics. Estuar Coast Shelf Sci 79(1):143–151. doi:10.1016/j.ecss.2008.03.016

    Article  Google Scholar 

  • Le Provost C, Genco ML, Lyard F (1994) Spectroscopy of the world ocean tides from a finite element hydrodynamic model. J Geophys Res 99:777–797

    Google Scholar 

  • Legrand S, Deleersnijder E, Hanert E, Legat V, Wolanski E (2006) High-resolution, unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia. Estuar Coast Shelf Sci 68:36–46

    Article  Google Scholar 

  • Legrand S, Legat V, Deleersnijder E (2000) Delaunay mesh generation for an unstructured-grid ocean circulation model. Ocean Model 2:17–28

    Article  Google Scholar 

  • Lietaer O, Fichefet T, Legat V (2008) The effects of resolving the Canadian Arctic Archipelago in a finite element sea ice model. Ocean Model 24:140–152. doi:10.1016/j.ocemod.2008.06.002

    Article  Google Scholar 

  • Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: modern insights from FES2004. Ocean Dyn 56:394–415

    Article  Google Scholar 

  • National Geographic Data Center (2006) ETOPO1 global relief model. http://www.ngdc.noaa.gov/mgg/global/global.html.

  • Piggott M, Gorman G, Pain C (2007) Multi-scale ocean modelling with adaptive unstructured grids. CLIVAR Exch Ocean Model Dev Assess 12(42):21–23 (http://eprints.soton.ac.uk/47576/)

    Google Scholar 

  • Rebay S (1993) Efficient unstructured mesh generation by means of delaunay triangulation and Bowyer-Watson algorithm. J Comput Phys 106:25–138

    Article  Google Scholar 

  • Weatherill NP (1990) The integrity of geometrical boundaries in the two-dimensional delaunay triangulation. Commun Appl Numer Methods 6(2):101–109

    Article  Google Scholar 

  • Wessel P, Smith WHF (1996) A global self-consistent, hierarchical, high-resolution shoreline database. J Geophys Res 101(B4):8741–8743. http://www.soest.hawaii.edu/wessel/gshhs/gshhs.html

    Article  Google Scholar 

  • White L, Deleersnijder E, Legat V (2008) A three-dimensional unstructured mesh finite element shallow-water model, with application to the flows around an island and in a wind-driven elongated basin. Ocean Model 22:26–47

    Article  Google Scholar 

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Acknowledgements

The present study was carried out within the scope of the project A second-generation model of the ocean system, which is funded by the Communauté Française de Belgique, as Actions de Recherche Concertées, under contract ARC 04/09-316. This work is a contribution to the SLIMFootnote 2 project.

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Correspondence to Jonathan Lambrechts.

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Responsible Editor: Pierre Lermusiaux

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Lambrechts, J., Comblen, R., Legat, V. et al. Multiscale mesh generation on the sphere. Ocean Dynamics 58, 461–473 (2008). https://doi.org/10.1007/s10236-008-0148-3

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