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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013005024
pages 463-495

AN EFFICIENT COARSE GRID PROJECTION METHOD FOR QUASIGEOSTROPHIC MODELS OF LARGE-SCALE OCEAN CIRCULATION

Omer San
Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA
Anne E. Staples
Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA

ABSTRACT

This paper puts forth a coarse grid projection (CGP) multiscale method to accelerate computations of quasigeostrophic (QG) models for large-scale ocean circulation. These models require solving an elliptic subproblem at each time step, which takes the bulk of the computational time. The method we propose here is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for solving the elliptic subproblem and potential vorticity equations in the QG flow solvers. After solving the elliptic subproblem on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. The potential vorticity field is then updated on the fine grid with savings in computational time due to the reduced number of grid points for the elliptic solver. The method is applied to both single-layer barotropic and two-layer stratified QG ocean models for mid-latitude oceanic basins in the beta plane, which are standard prototypes of more realistic ocean dynamics. The method is found to accelerate these computations while retaining the same level of accuracy in the fine-resolution field. A linear acceleration rate is obtained for all the cases we consider due to the efficient linear-cost, fast Fourier transform-based elliptic solver used. We expect the speed-up of the CGP method to increase dramatically for versions of the method that use other suboptimal, elliptic solvers, which are generally quadratic cost. It is also demonstrated that numerical oscillations due to lower grid resolutions, in which the Munk scales are not resolved adequately, are effectively eliminated with CGP method.

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