northwestern European continental shelf; Delaunay triangulation; finite elements methods; finite volumes methods; unstructured grids
Abstract :
[en] A new mesh refinement strategy for generating high quality unstructured meshes of the Northwestern European continental shelf, the continental slope and the neighbouring ocean is presented. Our objective is to demonstrate the ability of anisotropic unstructured meshes to adequately address the challenge of simulating the hydrodynamics occurring in these three regions within a unique mesh. The refinement criteria blend several hydrodynamic considerations as the tidal wave propagation on the continental shelf and the hydrostatic consistency condition in steep areas. Several meshes illustrate both the validity and the efficiency of the refinement strategy. The selection of the refinement parameters is discussed. Finally, an attempt is made to take into account tidal ellipses, providing another cause for anisotropy in the mesh. (c) 2007 Elsevier Ltd. All rights reserved.
Research center :
MARE - Centre Interfacultaire de Recherches en Océanologie - ULiège
Disciplines :
Earth sciences & physical geography
Author, co-author :
Legrand, Sebastien
Deleersnijder, Eric
Delhez, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Mathématiques générales
Legat, Vincent
Language :
English
Title :
Unstructured, anisotropic mesh generation for the Northwestern European continental shelf, the continental slope and the neighbouring ocean
Publication date :
2007
Journal title :
Continental Shelf Research
ISSN :
0278-4343
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Adcroft A., and Hallberg R. On methods for solving the oceanic equations of motion in generalized vertical coordinates. Ocean Modelling 11 (2004) 224-233
Adcroft A., and Marshall D. How slippery are piecewise-constant coastlines in numerical models?. Tellus 50A (1998) 95-108
Beckmann A., and Haidvogel D. Numerical simulation of flow around a tall isolated seamount. Part I: problem formulation and model accuracy. Journal of Physical Oceanography 23 (1993) 1736-1753
Bell M.J., Forbes R.M., and Hines A. Assessment of the FOAM global data assimilation system for real-time operational ocean forecasting. Journal of Marine Systems 25 (2000) 1-22
Biscaye P.E., Flagg C.N., and Falkowski P.G. The shelf edge exchange processes experiment, SEEP-II: an introduction to hypotheses, results and conclusions. Deep Sea Research II 41 (1994) 231-252
Chanut J., and Etienne H. Forcing coastal model with MERCATOR data. Mercator Ocean Quarterly Newsletter 18 (2005) 2-3
Coelho H.S., Neves R.J.J., White M., Leito P.C., and Santos A.J. A model for ocean circulation on the Iberian coast. Journal of Marine Systems 32 1-3 (2002) 153-179
Davies A.M., and Jones J.E. Sensitivity of tidal bed stress distributions, near-bed currents, overtides, and tidal residuals to frictional effects in the eastern irish sea. Journal of Physical Oceanography 26 (1996) 2553-2575
Davies A.M., and Xing J. Processes influencing sediment movement on the Malin-Hebrides shelf. Continental Shelf Research 22 (2002) 2081-2113
Davies A.M., and Xing J. On the interaction between internal tides and wind induced near inertial currents at the shelf edge. Journal of Geophysical Research 108 C3 (2003) 3099
Davies A.M., and Xing J. Modelling process influencing shelf edge exchange of water and suspended sediment. Continental Shelf Research 25 (2005) 973-1001
Deleersnijder E., and Beckers J.-M. On the use of σ-coordinate in regions of large bathymetric variations. Journal of Marine Systems 3 (1992) 381-390
Deleersnijder E., and Ruddick K.G. A generalized vertical coordinate for 3D marine models. Bulletin de la Société Royale des Sciences de Liège 61 6 (1992) 489-502
Dompierre, J., Vallet, M.-G., Labb, P., Guibault, F., 2003. On simplex shape measures with extension for anisotropic meshes. In: Workshop on Mesh Quality and Dynamic Meshing. Sandia National Laboratories, Livermore, CA, pp. 46-71.
Foreman M.G.G., Walters R.A., Henry R.F., Keller C.P., and Dolling A.G. A tidal model for eastern Juan de Fuca Strait and the southern Strait of Georgia. Journal of Geophysical Research 100 C1 (1995) 721-740
Frey P., and George P. Mesh Generation: Application to Finite Elements (2000), Hermes Science Publishing
Frey W. Selective refinement: a new strategy for automatic node placement in graded triangular meshes. International Journal for Numerical Methods in Engineering 24 11 (1987) 2183-2200
Gerritsen H., de Vries J.W., and Philippart M.E. The Dutch continental shelf model. Quantitative Skill Assessment for Coastal Ocean Models, Coastal and Estuarine Studies 48 (1995) 425-467
Gorman, G.J., Piggott, M.D., Pain, C.C., de Oliveira, C.R.E., Umpleby, A.P., Goddard, A.J.H., 2006. Optimisation based bathymetry approximation through constrained unstructured mesh adaptivity. Ocean Modelling 12 (3-4), 436-452.
Hagen S.C., Westerink J.J., Kolar R.L., and Horstmann O. Two-dimensional, unstructured mesh generation for tidal models. International Journal for Numerical Methods in Fluids 35 (2001) 669-686
Hall P., and Davies A.M. Comparison of finite difference and element models of internal tides on the malin-hebrides shelf. Ocean Dynamics 55 (2005) 272-293
Hanert E., Le Roux D.Y., Legat V., and Deleersnijder E. An efficient Eulerian finite element for the shallow water equations. Ocean Modelling 10 (2005) 115-136
Haney R.L. On the pressure gradient force over steep topography in sigma coordinate ocean models. Journal of Physical Oceanography 21 (1991) 610-619
Henry R., and Walters R. Geometrically based, automatic generator for irregular networks. Communications in Numerical Methods in engineering 9 (1993) 555-566
Holt J.T., Proctor R., Blackford J.C., Allen J.I., and Ashworth M. Advective controls on primary production in the stratified western Irish Sea: an eddy-resolving model study. Journal of Geophysical Research 109 (2004) 5024
Holt J.T., Allen J.I., Proctor R., and Gilbert F. Error quantification of a high-resolution coupled hydrodynamic-ecosystem coastal-ocean model: Part 1 model overview and assessment of the hydrodynamics. Journal of Marine Systems 57 1-2 (2005) 167-188
Huthnance J.M. Circulation, exchange and water masses at the ocean margin the role of physical processes at the shelf edge. Progress in Oceanography 35 (1995) 353-431
Janjic Z.I. Pressure gradient force and advection scheme used for forecasting with steep and small scale topography. Contributions to Atmospheric Physics 50 (1977) 186-199
Jarosz E., Blain C.A., Murray S.P., and Inoue M. Barotropic tides in the Bab el Mandab Straits-numerical simulations. Continental Shelf Research 25 (2005) 1225-1247
Kasahara A. Various vertical coordinate systems used for numerical weather predictions. Monthly Weather Review 102 (1974) 509-522
Lamb K.G. Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. Journal of Geophysical Research 99 C1 (1994) 843-864
Lamb K.G. Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophysical Research Letters 31 L09313 (2004) doi:10.1029/2003GL019393
Legg S. Internal tides generated on a corrugated continental slope. Part I: cross-slope barotropic forcing. Journal of Physical Oceanography 34 (2004) 156-173
Legg S. Internal tides generated on a corrugated continental slope. Part II: along-slope barotropic forcing. Journal of Physical Oceanography 34 (2004) 1824-1838
Legrand S., Legat V., and Deleersnijder E. Delaunay mesh generation for an unstructured-grid ocean general circulation model. Ocean Modelling 2 (2000) 17-28
Legrand, S., Deleersnijder, E., Hanert, E., Legat, V., Wolanski, E., 2006. High-resolution unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia. Estuarine, Coastal and Shelf Science 68 (1-2), 36-46.
Luyten, P.J., Jones, J.E., Proctor, R., Tabor, A., Tett, P., Wild-Allen, K., 1999. Coherens-a coupled hydrodynamical-ecological model for regional and shelf seas: User documentation. Mumm Report, Management Unit of the Mathematical Models of the North Sea.
Lynch, D.R., Naimie, C.E., Smith, K.W., 2003. Tidal atlas for the Irish Shelf Seas. Numerical Methods Laboratory Report NML-03-7, Dartmouth College, Hanover NH USA.
Lynch D.R., Smith K.W., and Cahill B. Seasonal mean circulation on the Irish shelf a model-generated climatology. Continental Shelf Research 24 (2004) 2215-2244
Mesinger F. On the convergence and error problems of the calculation of the pressure gradient force in sigma coordinate models. Geophysical, Astrophysical Fluid Dynamics 19 (1982) 105-117
National Geophysical Data Center, 1988. Digital relief of the surface of the earth. Technical Report Data Announcement 88-MGG-02, NOAA, Boulder.
Pietrzak, J., Deleersnijder, E., Schroeter, J. (Eds.), 2005. The Second International Workshop on Unstructured Mesh Numerical Modelling of Coastal, Shelf and Ocean Flows. Ocean Modelling 10(1-2), 1-252 (special issue).
Proctor R., Chen F., and Tett P.B. Carbon and nitrogen fluxes across the Hebridean shelf break, estimated by 2D coupled physical-microbiological model. Science of the Total Environment 314-316 (2003) 787-800
Shchepetkin A.F., and McWilliams J.C. A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate. Journal of Geophysical Research 108 C3 (2003) 3090
Shewchuk, J.R., 1996. Triangle: engineering a 2d quality mesh generator and delaunay triangulator. In: First Workshop on Applied Computational Geometry. Association for Computing Machinery, Philadelphia, PA, pp. 124-133.
Skogen M.D., Svendsen E., Berntsen J., Aksnes D.L., and Ulvestad K.B. Modelling the primary production in the North Sea using a coupled 3-dimensional physical chemical biological ocean model. Estuarine, Coastal and Shelf Science 41 (1995) 545-565
Souza A.J., Simpson J.H., Harikrishnan M., and Malarkey J. Flow structure and seasonability in the Hebridean slope current. Oceanolagy Acta 24 (2001) S63-S76
Thompson J.F., Warsi Z.U.A., and Mastin C.W. Numerical Grid Generation. Foundations and Applications (1985), North-Holland, Amsterdam
Walsh J.J. Importance of continental margins in the marine biogeochemical cycling of carbon and nitrogen. Nature 350 6313 (1991) 53-55
Walsh J.J., Biscaye P.E., and Csanady G.T. The 1983-1984 Shelf Edge Exchange Processes (Seep-I): hypotheses and highlights. Continental Shelf Research 8 (1988) 435-456
Walters R. Coastal ocean models: two useful finite element methods. Continental Shelf Research 25 (2005) 775-793
Watson D. Computing the n-dimensional Delaunay tesselation with applications to Voronoi polytopes. Computer Journal 24 2 (1981) 167-172
Wollast R., and Chou L. Ocean margin exchange in the Northern Gulf of Biscay: OMEX I an introduction. Deep Sea Res. II 48 14/15 (2001) 2971-2978
Xing J., and Davies A.M. The influence of wind effects upon internal tides in the shelf edge regions. Journal of Physical Oceanography 27 (1997) 2100-2125
Xing J., and Davies A.M. Formulation of a three-dimensional shelf edge model and its application to inertial tide generation. Continental Shelf Research 18 2-4 (1998) 405-440
Xing, J., Davies, A.M., 1998b. A three-dimensional model of internal tides on the malin-hebrides shelf and shelf edge. Journal of Geophysical Research 103(C12), 27,821-27,847.
Xing J., Chen F., and Proctor R. A two-dimensional slice model of the shelf edge region off the west coast of Scotland: model response to realistic seasonal forcing and the role of M2 tide. Continental Shelf Research 19 10 (1999) 1353-1386
