Cell-vertex discretization of shallow water equations on mixed unstructured meshes

详细信息    查看全文

• 作者：S. Danilov (1) (2)
  A. Androsov (1)
  
  1. Alfred Wegener Institute ; Helmholtz Centre for Polar and Marine Research ; Postfach 12-01-61 ; 27515 ; Bremerhaven ; Germany
  2. A. M. Obukhov Institute of Atmospheric Physics ; RAS ; Pyzhevsky per. ; 3 ; 119017 ; Moscow ; Russia
  
• 关键词：Unstructured mixed meshes ; Finite ; volume discretization ; Shallow water equations ; Filter operators ; Numerical stability ; Tides
• 刊名：Ocean Dynamics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：65
• 期：1
• 页码：33-47
• 全文大小：3,490 KB
• 参考文献：1. Andersen OB (2008) Personal communication
  2. Androsov AA, Kagan BA, Voltzinger NE (2002) Numerical modelling of barotropic tidal dynamics in the strait of Messina. Adv in Water Res 25:401鈥?15 CrossRef
  3. 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鈥?86 CrossRef
  4. Danilov S (2012) Two finite-volume unstructured mesh models for large-scale ocean modeling. Ocean Modell 47:14鈥?5 CrossRef
  5. Davies AM, Sauvel J, Evans J (1985) Computing near coastal tidal dynamics from observations and a numerical model. Cont Shelf Res 4 (3):341鈥?66 CrossRef
  6. Defant A (1961) Physical oceanography, vol II. Pergamon Press, New York
  7. Egbert G, Bennett A, Foreman M (1994) TOPEX/Poseidon tides estimated using a global inverse model. J of Geoph Res 99(C12):24821鈥?4852 CrossRef
  8. Kernkamp HWJ, Van Dam A, Stelling GS, de Coede ED (2011) Efficient scheme for the shallow water equations on unstructured grids with application to the continental shelf. Ocean Dyn 61:1175鈥?188 CrossRef
  9. 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鈥?60 CrossRef
  10. Le Roux DY (2012) Spurious inertial oscillations in shallow-water models. J Comput Phys 231:7959鈥?987 CrossRef
  11. Ma脽mann S, Androsov A, Danilov S (2010) Intercomparison between finite element and finite volume approaches to model North Sea tides. Cont Shelf Res 30:680鈥?91 CrossRef
  12. Ringler TD, Randall DA (2002) The ZM grid: an alternative to the Z grid. Mon Wea Rev 130:1411鈥?422 CrossRef
  13. 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鈥?404 CrossRef
  14. Stelling GS, Duinmeijer SPA (2003) A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int J for Numer Methods in Fluids 43(12):1329鈥?354 CrossRef
  15. Szmelter J, Smolarkiewicz P (2010) An edge-based unstructured mesh discretization in geospherical framework. J Comput Phys 229:4980鈥?995 CrossRef
  16. Thompson J F (ed) (1982) Numerical grid generation. Appl Math and Comput 10鈥?1:910
  17. Thuburn J, Ringler TD, Skamarock WC, Klemp JB (2009) Numerical representation of geostrophic modes on arbitrarily structured C-grids. J Comput Phys 228:8321鈥?335 CrossRef
  18. 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
  19. Zhang Y, Baptista AM (2008) SELFE A semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation. Ocean Model 21:71鈥?6 CrossRef
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Oceanography
  Geophysics and Geodesy
  Meteorology and Climatology
  Fluids
  Structural Foundations and Hydraulic Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1616-7228

文摘

Finite-volume discretizations can be formulated on unstructured meshes composed of different polygons. A staggered cell-vertex finite-volume discretization of shallow water equations is analyzed on mixed meshes composed of triangles and quads. Although triangular meshes are most flexible geometrically, quads are more efficient numerically and do not support spurious inertial modes of triangular cell-vertex discretization. Mixed meshes composed of triangles and quads combine benefits of both. In particular, triangular transitional zones can be used to join quadrilateral meshes of differing resolution. Based on a set of examples involving shallow water equations, it is shown that mixed meshes offer a viable approach provided some background biharmonic viscosity (or the biharmonic filter) is added to stabilize the triangular part of the mesh.