Ocean Dynamics

, Volume 63, Issue 1, pp 89–113 | Cite as

A three-dimensional discontinuous Galerkin model applied to the baroclinic simulation of Corpus Christi Bay

  • Vadym Aizinger
  • Jennifer Proft
  • Clint Dawson
  • Dharhas Pothina
  • Solomon Negusse
Article
Part of the following topical collections:
  1. Topical Collection on Multi-scale modelling of coastal, shelf and global ocean dynamics

Abstract

In this work, we present results of a numerical study of Corpus Christi Bay, Texas and surrounding regions and compare simulated model results to recorded data. The validation data for the year 2000 include the water elevation, velocity, and salinity at selected locations. The baroclinic computations were performed using the University of Texas Bays and Estuaries 3D (UTBEST3D) simulator based on a discontinuous Galerkin finite element method for unstructured prismatic meshes. We also detail some recent advances in the modeling capabilities of UTBEST3D, such as a novel turbulence scheme and the support for local vertical discretization on parts of the computational domain. All runs were conducted on parallel clusters; an evaluation of parallel performance of UTBEST3D is included.

Keywords

Shallow water equations Marine model Discontinuous Galerkin method Free surface Baroclinic processes 

References

  1. Aizinger V (2004) A discontinuous Galerkin method for two- and three-dimensional shallow-water equations. PhD thesis, University of Texas at AustinGoogle Scholar
  2. Aizinger V (2011) A geometry independent slope limiter for the discontinuous Galerkin method. In: Krause E et al (eds) Computational science and high performance computing IV. Notes on numerical fluid mechanics and multidisciplinary design, vol 115. Springer, Berlin, pp 207–217CrossRefGoogle Scholar
  3. Aizinger V, Dawson C (2002) A discontinuous Galerkin method for two-dimensional flow and transport in shallow water. Adv Water Resour 25:67–84CrossRefGoogle Scholar
  4. Aizinger V, Dawson C (2007) The local discontinuous Galerkin method for three-dimensional shallow water flow. Comput Methods Appl Mech Eng 196:734–746CrossRefGoogle Scholar
  5. Blaise S, Comblen R, Legat V, Remacle J-F, Deleersnijder E, Lambrechts J (2010) A discontinuous finite element baroclinic marine model on unstructured prismatic meshes. Part I: space discretization. Ocean Dyn 60:1371–1393CrossRefGoogle Scholar
  6. Canuto VM, Howard A, Cheng Y, Dubovikov MS (2001) Ocean turbulence. Part I: one-point closure model-momentum and heat vertical diffusivities. J Phys Oceanogr 31:1413–1426CrossRefGoogle Scholar
  7. Chen C, Liu H, Beardsley R (2003) An unstructured, finite-volume, three-dimensional, primitive equation ocean model: application to coastal ocean and estuaries. J Atmos Ocean Technol 20:159–186CrossRefGoogle Scholar
  8. Chippada S, Dawson CN, Martinez M, Wheeler MF (1998) A Godunov-type finite volume method for the system of shallow water equations. Comput Methods Appl Mech Eng 151:105–129CrossRefGoogle Scholar
  9. Cockburn B, Shu C-W (1989) TVB Runge–Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework. Math Comput 52:411–435Google Scholar
  10. Cockburn B, Shu C-W (1998) The local discontinuous Galerkin finite element method for convection-diffusion systems. SIAM J Numer Anal 35:2440–2463CrossRefGoogle Scholar
  11. Cockburn B, Karniadakis G, Shu C-W (2000) The development of discontinuous Galerkin methods. In: Cockburn B, Karniadakis G, Shu C-W (eds) Discontinuous Galerkin methods: theory, computation and applications. Lecture notes in computational science and engineering, vol 11, part I: overview. Springer, Berlin, pp 3–50CrossRefGoogle Scholar
  12. Dawson C, Aizinger V (2005) A discontinuous Galerkin method for three-dimensional shallow water equations. J Sci Comput 22–23(1–3):245–267CrossRefGoogle Scholar
  13. Dawson C, Proft J, Aizinger V (2011) UTBEST3D hydrodynamic model verification of Corpus Christi Bay. http://www.twdb.texas.gov/RWPG/rpgm_rpts/0904830896_UTBEST3D.pdf Accessed 17 July 2012
  14. Huang H (2011) Finite volume coastal ocean model (FVCOM) 3D hydrodynamic model comparison. http://www.twdb.state.tx.us/RWPG/rpgm_rpts/0904830891_OceanModel.pdf Accessed 17 July 2012
  15. Karypis G, Kumar V (1999) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20:359–392CrossRefGoogle Scholar
  16. Kuzmin D (2010) A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods. J Comput Appl Math 233:3077–3085CrossRefGoogle Scholar
  17. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys Space Phys 20:851–875CrossRefGoogle Scholar
  18. The Texas Water Development Board (2000) Corpus Christi Bay intensive inflow survey May 5–May 7, 2000. http://midgewater.twdb.state.tx.us/bays-estuaries/studies/cor00main.html Accessed 20 December 2011
  19. Toro EF, Spruce M, Speares W (1994) Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4:25–34CrossRefGoogle Scholar
  20. Umlauf L, Burchard H (2003) A generic length-scale equation for geophysical turbulence models. J Mar Res 61:235–265CrossRefGoogle Scholar
  21. Umlauf L, Burchard H (2005) Second-order turbulence closure models for geophysical boundary layers. A review of recent work. Cont Shelf Res 25:795–827CrossRefGoogle Scholar
  22. USGS (2001) Water budget for the Nueces Estuary, Texas, May–October 1998. USGS Fact Sheet 081-01, December (2001)Google Scholar
  23. Vreugdenhil CB (1994) Numerical methods for shallow-water flow. Kluwer, DordrechtGoogle Scholar
  24. Warner JC, Sherwood CR, Arango HG, Signell RP (2005) Performance of four turbulenc closure models implemented using a generic length scale method. Ocean Model 8:81–113CrossRefGoogle Scholar
  25. Zhang YJ (2010) Technical support—inter-model comparison for Corpus Christi Bay testbed. http://www.twdb.state.tx.us/RWPG/rpgm_rpts/0904830892.pdf. Accessed 17 July 2012
  26. Zhang Y-L, Baptista AM (2008) SELFE: a semi-implicit Eulerian–Lagrangian finite-element model for cross-scale ocean circulation. Ocean Model 21(3–4):71–96CrossRefGoogle Scholar
  27. Zhang Y-L, Baptista AM, Myers EP (2004) A cross-scale model for 3D baroclinic circulation in estuary-plume-shelf systems: I. Formulation and skill assessment. Cont Shelf Res 24:2187–2214CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vadym Aizinger
    • 1
  • Jennifer Proft
    • 2
  • Clint Dawson
    • 2
  • Dharhas Pothina
    • 3
  • Solomon Negusse
    • 3
  1. 1.University of Erlangen-NuernbergErlangenGermany
  2. 2.The University of Texas at AustinAustinUSA
  3. 3.Texas Water Development BoardAustinUSA

Personalised recommendations