Skip to main content
SpringerLink
Log in

Unstructured Meshes in Large-Scale Ocean Modeling

  • Reference work entry
  • First Online:
Handbook of Geomathematics

  • 4128 Accesses

Abstract

The current status of large-scale ocean modeling on unstructured meshes is discussed in the context of climate applications. Our review is based on FEOM, which is at present the only general circulation model on a triangular mesh with a proven record of global applications. Different setups are considered including some promising alternative finite-element and finite-volume configurations. The focus is on consistency and performance issues which are much easier to achieve with finite-volume methods. On the other hand, they sometimes suffer from numerical modes and require more research before they can be generally recommended for modeling of the general circulation.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,200.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Blaise S (2009) Development of a finite element marine model. Thesis, École polytechnique de Louvain, Université Catolique de Louvain

    Google Scholar 

  • Blazek J (2001) Computational fluid dynamics: principles and applications. Elsevier, Amsterdam/New York

    MATH  Google Scholar 

  • Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing – comparisons with observations. Geophys Res Lett 30:1275

    Article  Google Scholar 

  • Casulli V, Walters RA (2000) An unstructured grid, three-dimensional model based on the shallow water equations. Int J Numer Methods Fluids 32:331–348

    Article  MATH  Google Scholar 

  • Chen C, Liu H, Beardsley RC (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: applications to coastal ocean and estuaries. J Atmos Ocean Technol 20:159–186

    Article  Google Scholar 

  • Codina R, Soto O (1997) Finite element solution of the Stokes problem with dominating Coriolis force. Comput Methods Appl Mech Eng 142:215–234

    Article  MathSciNet  MATH  Google Scholar 

  • Codina R, Zienkiewicz OC (2002) CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as the stabilization parameter. Commun Numer Methods Eng 18:99–112

    Article  MATH  Google Scholar 

  • Comblen R, Legrand S, Deleersnijder E, Legat V (2009) A finite-element method for solving shallow water equations on the sphere. Ocean Model 28:12–23

    Article  Google Scholar 

  • Danilov S (2010) On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows. Ocean Dyn 60(6):1361–1369. doi: 10.1007/s10236-010-0339-6

    Article  Google Scholar 

  • Danilov S, Kivman G, Schröter J (2004) A finite element ocean model: principles and evaluation. Ocean Model 6:125–150

    Article  Google Scholar 

  • Danilov S, Wang Q, Losch M, Sidorenko D, Schröter J (2008) Modeling ocean circulation on unstructured meshes: comparison of two horizontal discretizations. Ocean Dyn 58:365–374

    Article  Google Scholar 

  • Dawson CN, Westerink JJ, Feyen JC, Pothina D (2006) Continuous, discontinuous and coupled discontinuous-continuous Galerkin finite element methods for the shallow water equations. Int J Numer Methods Fluids 52:63–88

    Article  MathSciNet  MATH  Google Scholar 

  • Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New York

    Book  Google Scholar 

  • Dupont F, Straub DN, Lin CA (2003) Influence of a step-like coastline on the basin scale vorticity budget in mid-latitude gyre models. Tellus 55A:255–272

    Article  Google Scholar 

  • Ford R, Pain CC, Piggott MD, Goddard AJH, de Oliveira CRE, Uplemby AP (2004) A non-hydrostatic finite-element model for three-dimensional stratified flows. Part I: model formulation. Mon Wea Rev 132:2832–2844

    Article  Google Scholar 

  • Fox-Kemper B, Menemenlis D (2008) Can large eddy simulation techniques improve mesoscale rich ocean models? In: Hecht MW, Hasumi H (eds) Ocean modeling in an eddying regime. Geophysical monograph, vol 177. AGU, Washington, DC, pp 319–337

    Chapter  Google Scholar 

  • Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Model 14:139–173

    Article  Google Scholar 

  • Haidvogel DB, Beckmann A (1999) Numerical ocean circulation modeling. Imperial College Press, London

    MATH  Google Scholar 

  • Hua BL, Thomasset F (1984) A noise-free finite-element scheme for the two-layer shallow-water equations. Tellus 36A:157–165

    Article  MathSciNet  Google Scholar 

  • Iskandarani M, Haidvogel DV, Levin JC (2003) A three-dimensional spectral element model for the solution of the hydrostatic primitive equations. J Comput Phys 186:397–425

    Article  MathSciNet  MATH  Google Scholar 

  • Gent PR, McWilliams JC (1990) Isopycnal mixing in ocean circulation models. J Phys Oceanogr 20:150–155

    Article  Google Scholar 

  • Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Griffies SM, Adcroft AJ (2008) Formulating the equations of ocean models. In: Hecht MW, and Hasumi H, (eds) Ocean modeling in an eddying regime. Geophysical monograph, vol 177. AGU, Washington, DC, pp 281–317

    Chapter  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 modelling. Ocean Model 2:123–192

    Article  Google Scholar 

  • Hervouet J-M (2000) TELEMAC modelling system: an overview. Hydrol Process 14:2209–2210

    Article  Google Scholar 

  • Hervouet J-M (2007) Hydrodynamics of free surface flows: modelling with the finite element method. Wiley, New York

    Book  MATH  Google Scholar 

  • Jackett DR, McDougall TJ (1995) Minimal adjustment of hydrographic profiles to achieve static stability. J Atmos Ocean Technol 12:381–389

    Article  Google Scholar 

  • Jones JE, Davies AM (2008) Storm surge computations for the west coast of Britain using a finite element model (TELEMAC). Ocean Dyn 58:337–363

    Article  Google Scholar 

  • Kobayashi MH, Pereira JMC, Pereira JCF (1999) A conservative finite-volume second-order accurate projection method on hybrid unstructured grids. J Comput Phys 150:40–75

    Article  MathSciNet  MATH  Google Scholar 

  • Le Roux DY, Sène A, Rostand V, Hanert E (2005) On some spurious mode issues in shallow-water models using a linear algebra approach. Ocean Model 10:83–94

    Article  Google Scholar 

  • Le Roux DY, Rostand V, Pouliot B (2007) Analysis of numerically induced oscillations in 2D finite-element shallow water models. Part I: inertia-gravity waves. SIAM J Sci Comput 29:331–360

    Article  MathSciNet  MATH  Google Scholar 

  • Löhner R, Morgan K, Peraire J, Vahdati M (1987) Finite-element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations. Int J Numer Methods Fluids 7:1093–1109

    Article  MATH  Google Scholar 

  • Lynch DR, Ip JTC, Naimie, CE, Werner FE (1996) Comprehensive coastal circulation model with application to the Gulf of Maine. Cont Shelf Res 16:875–906

    Article  Google Scholar 

  • Lynch DR, Holbroke MJ, Naimie CE (1997) The Maine coastal current: spring climatological circulation. Cont Shelf Res 17:605–634

    Article  Google Scholar 

  • Marchesiello P, McWilliams JC, Shchepetkin A (2001) Open boundary conditions for long-term integration of regional oceanic models. Ocean Model 3:1–20

    Article  Google Scholar 

  • Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997) A finite-volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers. J Geophys Res 102:5753–5766

    Article  Google Scholar 

  • Pain CC, Piggott MD, Goddard AJH, Fang F, Gorman GJ, Marshall DP, Eaton MD, Power PW, de Oliveira CRE (2005) Three-dimensional unstructured mesh ocean modelling, Ocean Model 10:5–33

    Article  Google Scholar 

  • Piggott MD, Pain CC, Gorman GJ, Marshall DP, Killworth PD (2008) Unstructured adaptive meshes for ocean modeling. In: Hecht MW, Hasumi H (eds) Ocean modeling in an eddying regime. Geophysical monograph, vol 177. AGU, Washington, DC, pp 383–408

    Chapter  Google Scholar 

  • Raviart P, Thomas J (1977) A mixed finite element method for 2nd order elliptic problems. In: Galligani I, Magenes E (eds) Mathematical aspects of the finite element methods. Lecture notes in mathematics, vol 606. Springer, Berlin, pp 292–315

    Chapter  Google Scholar 

  • Shchepetkin AF, McWilliams JC (2005) The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Model 9:347–404

    Article  Google Scholar 

  • Stuhne GR, Peltier WR (2006) A robust unstructured grid discretization for 3-dimensional hydrostatic flows in spherical geometry: a new numerical structure for ocean general circulation modeling. J Comput Phys 213:704–729

    Article  MathSciNet  MATH  Google Scholar 

  • Timmermann R, Danilov S, Schröter J, Böning C, Sidorenko D, Rollenhagen K (2009) Ocean circulation and sea ice distribution in a finite-element global ice-ocean model. Ocean Model 27:114–129

    Article  Google Scholar 

  • Walters RA (2005) Coastal ocean models: two useful finite-element methods. Cont Shelf Res 25:775–793

    Article  Google Scholar 

  • Wang Q, Danilov S, Schröter J (2008) Finite element ocean circulation model based on triangular prismatic elements, with application in studying the effect of topography representation. J Geophys Res 113:C05015. doi: 10.1029/2007JC004482

    Google Scholar 

  • Wang B, Fringer OB, Giddings SN, Fong DA (2009a) High-resolution simulations of a macrotidal estuary using SUNTANS. Ocean Model 28:167–192

    Article  Google Scholar 

  • Wang Q, Danilov S, Schröter J (2009b) Bottom water formation in the southern Weddell Sea and the influence of submarine ridges: idealized numerical simulations. Ocean Model 28:50–59

    Article  Google Scholar 

  • Wang Q, Danilov S, Hellmer H, Schröter J (2010) Overflow dynamics and bottom water formation in the western Ross Sea: The influence of tides J Geophys Res 115, C10054. doi: 10.1029/2010JC006189

    Article  Google Scholar 

  • Westerink JJ, Luettich RA, Blain CA, Scheffner NW (1992) ADCIRC: an advanced three-dimensional circulation model for shelves, coasts and estuaries; Report 2: Users Manual for ADCIRC-2DDI. Contractors Report to the US Army Corps of Engineers, Washington, DC

    Google Scholar 

  • White L, Deleersnijder E, Legat V (2008a) A three-dimensional unstructured mesh 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 

  • White L, Legat V, Deleersnijder E (2008b) Tracer conservation for three-dimensional, finite element, free-surface, ocean modeling on moving prismatic meshes. Mon Weather Rev 136:420–442. doi: 10.1175/2007MWR2137.1

    Article  Google Scholar 

  • Yang Z, Khangaonkar T (2009) Modeling tidal circulation and stratification in Skagit River estuary using an unstructured grid ocean model. Ocean Model 28:34–49

    Article  Google Scholar 

  • Zhang Y, Baptista AM (2008) SELFE: a semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation. Ocean Model 21:71–96

    Article  Google Scholar 

  • Zienkiewicz OC, Taylor RL (2000a) The finite element method, vol 1. Butterworth-Heinemann, Oxford

    MATH  Google Scholar 

  • Zienkiewicz OC, Taylor RL (2000b) The finite element method vol 3: fluid dynamics. Butterworth-Heinemann, Oxford

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

    Sergey Danilov & Jens Schröter

Authors
  1. Sergey Danilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Schröter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergey Danilov .

Editor information

Editors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Danilov, S., Schröter, J. (2015). Unstructured Meshes in Large-Scale Ocean Modeling. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_13

Download citation

Publish with us

Policies and ethics

Search

Navigation