• Barnier, B., B. L. Hua, and C. Le Provost, 1991: On the catalytic role of high baroclinic modes in eddy-driven large-scale circulations. J. Phys. Oceanogr.,21, 976–997.

  • Berger, M., and J. Oliger, 1984: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys.,53, 484–512.

  • ——, and P. Colella, 1989: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys.,82, 64–84.

  • ——, and I. Rigoutsos, 1991: An algorithm for point clustering and grid generation. IEEE Trans. Systems Man Cybernetics,21, 1278–1286.

  • Fix, G. J., 1975: Finite element models for ocean circulation problems. SIAM J. Appl. Math.,29, 371–387.

  • Flierl, G. R., V. D. Larichev, J. C. McWilliams, and G. M. Reznik, 1980: The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Oceans,5, 1–41.

  • Fox, A. D., and S. J, Maskell, 1995: Two-way interactive nesting of primitive equation ocean models with topography. J. Phys. Oceanogr.,25, 2977–2996.

  • ——, and ——, 1996: A nested primitive equation model of the Iceland–Faeroe front. J. Geophys. Res.,101, 18 259–18 278.

  • Haidvogel, D. B., A. R. Robinson, and E. F. Schulman, 1980: The accuracy, efficiency and stability of three numerical models with application to open ocean problems. J. Comput. Phys.,34, 1–53.

  • Holland, W. R., 1978: The role of mesoscale eddies in the general circulation of the ocean. Numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanogr.,8, 363–392.

  • Kurihara, Y. G., G. J. Tripoli, and M. A. Bender, 1979: Design of a movable nested-mesh primitive equation model. Mon. Wea. Rev.,107, 239–249.

  • Laugier, M., P. Angot, and L. Mortier, 1996: Nested grid methods for an ocean model: A comparative study. Int. J. Num. Meth. Fluids,23, 1163–1195.

  • Le Provost, C., M. L. Genco, F. Lyard, P. Vincent, and P. Canceil, 1994a: Spectroscopy of the world ocean tides from a finite element hydrodynamic model. J. Geophys. Res.,99, 24 777–24 797.

  • ——, C. Bernier, and E. Blayo, 1994b: An intercomparison of two numerical methods for integrating a quasi-geostrophic multilayer model of ocean circulations: Finite element and finite difference methods. J. Comput Phys.,110, 341–359.

  • Le Roux, D. Y., A. Staniforth, and C. A. Lin, 1998: Finite elements for shallow-water equation ocean models. Mon. Wea. Rev.,126, 1931–1951.

  • Lynch, D. R., and F. E. Werner, 1987: Three-dimensional hydrodynamics on finite elements. Part I: Linearized harmonic model. Int. J. Num. Meth. Fluids,7, 871–909.

  • ——, and ——, 1991: Three-dimensional hydrodynamics on finite elements. Part II: Nonlinear time-stepping model. Int. J. Num. Meth. Fluids,12, 507–533.

  • Marchuk, G., and V. Shaydourov, 1983: Difference Methods and Their Extrapolations. Springer, 364 pp.

  • Oey, L.-Y., and P. Chen, 1992: A nested grid ocean model with application to the simulation of meanders and eddies in the Norwegian coastal current. J. Geophys. Res.,97, 20 063–20 086.

  • Peggion, G., 1994: Numerical inaccuracies across the interface of a nested grid. Numerical Meth. Part. Diff. Eq.,10, 455–473.

  • Perkins, A. L., L. F. Smedstad, D. W. Blake, G. W. Heburn, and A. J. Wallcraft, 1997: A new nested boundary condition for a primitive equation ocean model. J. Geophys. Res.,102, 3483–3500.

  • Schmitz, W. J., and W. R. Holland, 1982: A preliminary comparison of selected numerical eddy-resolving general circulation experiments with observations. J. Mar. Res.,40, 75–117.

  • Skamarock, W. C., and J. B. Klemp, 1993: Adaptive grid refinement for 2D and 3D nonhydrostatic atmospheric flows. Mon. Wea. Rev.,121, 788–804.

  • ——, J. Oliger, and R. L. Street, 1989: Adaptive grid refinement for numerical weather prediction. J. Comput. Phys.,80, 27–60.

  • Spall, M. A., and W. R. Holland, 1991: A nested primitive equation model for oceanic applications. J. Phys. Oceanogr.,21, 205–220.

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Adaptive Mesh Refinement for Finite-Difference Ocean Models: First Experiments

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  • 1 Projet IDOPT, Laboratoire de Modélisation et Calcul, Université Joseph Fourier, Grenoble, France
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Abstract

The application of an adaptive mesh refinement (AMR) method for structured mesh is examined in the context of ocean modeling. This method can be used with existing finite-difference ocean models at little computational and programming cost. Some first experiments in academic cases are presented in order to give some insight to the two following questions: (i) Is the AMR method appropriate and efficient for integration of numerical ocean circulation models (and particularly for long-term integration)? (ii) Can the AMR method be an efficient alternative to the classical zoom techniques for local prediction?

Numerical simulations are performed in the well-known case of the barotropic modon and in the case of a multilayered quasigeostrophic box model. They demonstrate that the use of the AMR method results in a very significant gain in CPU time (by a factor of 3) while conserving, within a 10%–20% range, the main statistical features of the solution obtained with a uniformly high resolution. For the problem of local prediction, it appears that only one simulation with the AMR method leads to better local predictions than classical nested grid techniques, wherever the region of interest is located, and for a comparable amount of computation. Further investigations are presently under way to generalize this application to basin-scale primitive equation models in realistic configurations and investigate whether or not these results are still valid.

Corresponding author address: Dr. Eric Blayo, Laboratoire de Modélisation et de Calcul, Institut de Mathematiques Appliquées de Grenoble, BP 53, 38041 Grenoble Cedex 9, France.

Email: Eric.Blayo@imag.fr

Abstract

The application of an adaptive mesh refinement (AMR) method for structured mesh is examined in the context of ocean modeling. This method can be used with existing finite-difference ocean models at little computational and programming cost. Some first experiments in academic cases are presented in order to give some insight to the two following questions: (i) Is the AMR method appropriate and efficient for integration of numerical ocean circulation models (and particularly for long-term integration)? (ii) Can the AMR method be an efficient alternative to the classical zoom techniques for local prediction?

Numerical simulations are performed in the well-known case of the barotropic modon and in the case of a multilayered quasigeostrophic box model. They demonstrate that the use of the AMR method results in a very significant gain in CPU time (by a factor of 3) while conserving, within a 10%–20% range, the main statistical features of the solution obtained with a uniformly high resolution. For the problem of local prediction, it appears that only one simulation with the AMR method leads to better local predictions than classical nested grid techniques, wherever the region of interest is located, and for a comparable amount of computation. Further investigations are presently under way to generalize this application to basin-scale primitive equation models in realistic configurations and investigate whether or not these results are still valid.

Corresponding author address: Dr. Eric Blayo, Laboratoire de Modélisation et de Calcul, Institut de Mathematiques Appliquées de Grenoble, BP 53, 38041 Grenoble Cedex 9, France.

Email: Eric.Blayo@imag.fr

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