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2010 | OriginalPaper | Chapter

13. Unstructured Meshes in Large-Scale Ocean Modeling

Authors : Sergey Danilov, Jens Schröter

Published in: Handbook of Geomathematics

Publisher: Springer Berlin Heidelberg

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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.

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Literature
go back to reference Blaise S (2009) Development of a finite element marine model. Thesis. École polytechnique de Louvain. Université Catolique de Louvain Blaise S (2009) Development of a finite element marine model. Thesis. École polytechnique de Louvain. Université Catolique de Louvain
go back to reference Blazek J (2001) Computational fluid dynamics: Principles and applications. Elsevier Blazek J (2001) Computational fluid dynamics: Principles and applications. Elsevier
go back to reference 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 30:1275CrossRef 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 30:1275CrossRef
go back to reference Casulli V, Walters RA (2000) An unstructured grid, three-dimensional model based on the shallow water equations. Int J Numer Meth Fluids 32: 331–348MATHCrossRef Casulli V, Walters RA (2000) An unstructured grid, three-dimensional model based on the shallow water equations. Int J Numer Meth Fluids 32: 331–348MATHCrossRef
go back to reference 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 Tech 20:159–186CrossRef 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 Tech 20:159–186CrossRef
go back to reference Codina R, Soto O (1997) Finite element solution of the Stokes problem with dominating Coriolis force. Comput Methods Appl Mech Eng 142: 215–234MATHCrossRefMathSciNet Codina R, Soto O (1997) Finite element solution of the Stokes problem with dominating Coriolis force. Comput Methods Appl Mech Eng 142: 215–234MATHCrossRefMathSciNet
go back to reference 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 18:99–112MATHCrossRef 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 18:99–112MATHCrossRef
go back to reference Comblen R, Legrand S, Deleersnijder E, Legat V (2009) A finite-element method for solving shallow water equations on the sphere. Ocean Modelling 28:12–23CrossRef Comblen R, Legrand S, Deleersnijder E, Legat V (2009) A finite-element method for solving shallow water equations on the sphere. Ocean Modelling 28:12–23CrossRef
go back to reference Danilov S, Kivman G, Schröter J (2004) A finite element ocean model: principles and evaluation. Ocean Modell 6:125-150CrossRef Danilov S, Kivman G, Schröter J (2004) A finite element ocean model: principles and evaluation. Ocean Modell 6:125-150CrossRef
go back to reference Danilov S, Wang Q, Losch M, Sidorenko D, Schröter J (2008) Modeling ocean circulation on unstructured meshes: comparison of two horizontal discretizations. Ocean Dynamics 58: 365–374CrossRef Danilov S, Wang Q, Losch M, Sidorenko D, Schröter J (2008) Modeling ocean circulation on unstructured meshes: comparison of two horizontal discretizations. Ocean Dynamics 58: 365–374CrossRef
go back to reference Danilov S (2010) On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows. Submitted to Ocean Dynamics Danilov S (2010) On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows. Submitted to Ocean Dynamics
go back to reference 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 52:63-88MATHCrossRefMathSciNet 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 52:63-88MATHCrossRefMathSciNet
go back to reference Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New YorkCrossRef Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New YorkCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Fox-Kemper B, Menemenlis D (2008) Can large eddy simulation techniques improve mesoscale rich ocean models? In: Hecht MW, Hasumi H (ed) Ocean modeling in an eddying regime, Geophysical Monograph 177, AGU 2008, pp 319–337 Fox-Kemper B, Menemenlis D (2008) Can large eddy simulation techniques improve mesoscale rich ocean models? In: Hecht MW, Hasumi H (ed) Ocean modeling in an eddying regime, Geophysical Monograph 177, AGU 2008, pp 319–337
go back to reference Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Modell 14:139–173CrossRef Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Modell 14:139–173CrossRef
go back to reference Haidvogel DB, Beckmann A (1999): Numerical ocean circulation modeling. Imperial College Press, LondonMATHCrossRef Haidvogel DB, Beckmann A (1999): Numerical ocean circulation modeling. Imperial College Press, LondonMATHCrossRef
go back to reference Hua BL, Thomasset F (1984) A noise-free finite-element scheme for the two-layer shallow-water equations. Tellus 36A:157–165CrossRefMathSciNet Hua BL, Thomasset F (1984) A noise-free finite-element scheme for the two-layer shallow-water equations. Tellus 36A:157–165CrossRefMathSciNet
go back to reference Iskandarani M, Haidvogel DV, Levin JC (2003) A three-dimensional spectral element model for the solution of the hydrostatic primitive equations. J Comp Phys 186:397–425MATHCrossRefMathSciNet Iskandarani M, Haidvogel DV, Levin JC (2003) A three-dimensional spectral element model for the solution of the hydrostatic primitive equations. J Comp Phys 186:397–425MATHCrossRefMathSciNet
go back to reference Gent PR, McWilliams JC (1990) Isopycnal mixing in ocean circulation models. J Phys Oceanogr 20:150–155CrossRef Gent PR, McWilliams JC (1990) Isopycnal mixing in ocean circulation models. J Phys Oceanogr 20:150–155CrossRef
go back to reference 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 Modell 2:123–192CrossRef 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 Modell 2:123–192CrossRef
go back to reference Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, PrincetonMATH Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, PrincetonMATH
go back to reference 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 177, AGU 2008: 281–317 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 177, AGU 2008: 281–317
go back to reference Hervouet J-M (2000) TELEMAC modelling system: an overview. Hydrol Processes 14:2209–2210CrossRef Hervouet J-M (2000) TELEMAC modelling system: an overview. Hydrol Processes 14:2209–2210CrossRef
go back to reference Hervouet J-M (2007) Hydrodynamics of Free Surface Flows: Modelling with the Finite Element Method. Wiley, New YorkMATHCrossRef Hervouet J-M (2007) Hydrodynamics of Free Surface Flows: Modelling with the Finite Element Method. Wiley, New YorkMATHCrossRef
go back to reference Jackett DR, McDougall TJ (1995) Minimal adjustment of hydrographic profiles to achieve static stability. J Atmos Ocean Techn 12: 381–389CrossRef Jackett DR, McDougall TJ (1995) Minimal adjustment of hydrographic profiles to achieve static stability. J Atmos Ocean Techn 12: 381–389CrossRef
go back to reference Jones JE, Davies AM (2008) Storm surge computations for the west coast of Britain using a finite element model (TELEMAC). Ocean Dyn 58:337–363CrossRef Jones JE, Davies AM (2008) Storm surge computations for the west coast of Britain using a finite element model (TELEMAC). Ocean Dyn 58:337–363CrossRef
go back to reference 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 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
go back to reference 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 Modell 10:83–94CrossRef 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 Modell 10:83–94CrossRef
go back to reference 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 29:331–360MATH 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 29:331–360MATH
go back to reference 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 7:1093–1109MATHCrossRef 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 7:1093–1109MATHCrossRef
go back to reference Lynch DR, Ip JTC, Naimie, CE, Werner FE (1996) Comprehensive coastal circulation model with application to the Gulf of Maine. Cont Shelf Res 16:875–906CrossRef Lynch DR, Ip JTC, Naimie, CE, Werner FE (1996) Comprehensive coastal circulation model with application to the Gulf of Maine. Cont Shelf Res 16:875–906CrossRef
go back to reference Lynch DR, Holbroke MJ, Naimie CE (1997) The Maine coastal current: spring climatological circulation. Cont Shelf Res 17:605–634CrossRef Lynch DR, Holbroke MJ, Naimie CE (1997) The Maine coastal current: spring climatological circulation. Cont Shelf Res 17:605–634CrossRef
go back to reference Marchesiello P, McWilliams JC, Shchepetkin A (2001) Open boundary conditions for long-term integration of regional oceanic models. Ocean Modell 3:1–20CrossRef Marchesiello P, McWilliams JC, Shchepetkin A (2001) Open boundary conditions for long-term integration of regional oceanic models. Ocean Modell 3:1–20CrossRef
go back to reference 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 102:5753–5766CrossRef 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 102:5753–5766CrossRef
go back to reference 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 Modell 10:5–33CrossRef 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 Modell 10:5–33CrossRef
go back to reference 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 177, AGU, pp 383–408 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 177, AGU, pp 383–408
go back to reference Raviart P, Thomas J (1977) A mixed finite element method for 2nd order elliptic problems. In: Mathematical Aspects of the Finite Element Methods, Lecture Notes in Math. 606, I. Galligani and E. Magenes, Eds., 292–315, Springer-Verlag, Berlin Raviart P, Thomas J (1977) A mixed finite element method for 2nd order elliptic problems. In: Mathematical Aspects of the Finite Element Methods, Lecture Notes in Math. 606, I. Galligani and E. Magenes, Eds., 292–315, Springer-Verlag, Berlin
go back to reference Shchepetkin AF, McWilliams JC (2005) The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell 9:347–404CrossRef Shchepetkin AF, McWilliams JC (2005) The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell 9:347–404CrossRef
go back to reference 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 213:704–729MATHCrossRefMathSciNet 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 213:704–729MATHCrossRefMathSciNet
go back to reference 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 Modell 27: 114–129CrossRef 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 Modell 27: 114–129CrossRef
go back to reference Walters RA (2005) Coastal ocean models: two useful finite-element methods. Cont Shelf Res 25: 775–793CrossRef Walters RA (2005) Coastal ocean models: two useful finite-element methods. Cont Shelf Res 25: 775–793CrossRef
go back to reference 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:10.1029/2007JC004482CrossRef 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:10.1029/2007JC004482CrossRef
go back to reference Wang B, Fringer OB, Giddings SN, Fong DA (2009a) High-resolution simulations of a macrotidal estuary using SUNTANS. Ocean Modell 28: 167–192CrossRef Wang B, Fringer OB, Giddings SN, Fong DA (2009a) High-resolution simulations of a macrotidal estuary using SUNTANS. Ocean Modell 28: 167–192CrossRef
go back to reference 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 Modell 28:50–59CrossRef 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 Modell 28:50–59CrossRef
go back to reference Wang Q, Danilov S, Hellmer H, Schröter J (2010) Overflows over the western Ross Sea continental slope, Submitted to J Geophys Res Wang Q, Danilov S, Hellmer H, Schröter J (2010) Overflows over the western Ross Sea continental slope, Submitted to J Geophys Res
go back to reference 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 D.C. 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 D.C.
go back to reference 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 Modell 22:26-47CrossRef 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 Modell 22:26-47CrossRef
go back to reference White L, Legat V, Deleersnijder E (2008b) Tracer conservation for three-dimensional, finite element, free-surface, ocean modeling on moving prismatic meshes. Mon Wea Rev 136:420–442. doi:10.1175/2007MWR2137.1CrossRef White L, Legat V, Deleersnijder E (2008b) Tracer conservation for three-dimensional, finite element, free-surface, ocean modeling on moving prismatic meshes. Mon Wea Rev 136:420–442. doi:10.1175/2007MWR2137.1CrossRef
go back to reference Yang Z, Khangaonkar T (2009) Modeling tidal circulation and stratification in Skagit River estuary using an unstructured grid ocean model. Ocean Modell 28:34–49CrossRef Yang Z, Khangaonkar T (2009) Modeling tidal circulation and stratification in Skagit River estuary using an unstructured grid ocean model. Ocean Modell 28:34–49CrossRef
go back to reference Zhang Y, Baptista AM (2008) SELFE: A semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation. Ocean Modell 21:71–96CrossRef Zhang Y, Baptista AM (2008) SELFE: A semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation. Ocean Modell 21:71–96CrossRef
go back to reference Zienkiewicz OC, Taylor RL (2000) The finite element method. V. 1. Butterworth–Heinemann, Oxford Zienkiewicz OC, Taylor RL (2000) The finite element method. V. 1. Butterworth–Heinemann, Oxford
go back to reference Zienkiewicz OC, Taylor RL (2000) The finite element method vol. 3: Fluid dynamics. Butterworth–Heinemann, Oxford Zienkiewicz OC, Taylor RL (2000) The finite element method vol. 3: Fluid dynamics. Butterworth–Heinemann, Oxford
Metadata
Title
Unstructured Meshes in Large-Scale Ocean Modeling
Authors
Sergey Danilov
Jens Schröter
Copyright Year
2010
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-01546-5_13

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