A Diagnostic Stabilized Finite-Element Ocean Circulation Model
A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuska-Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity-pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars. The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets. (C) 2002 Elsevier Science Ltd. All rights reserved.
Nechaev, D. A.,
(2003). A Diagnostic Stabilized Finite-Element Ocean Circulation Model. Ocean Modelling, 5(1), 37-63.
Available at: https://aquila.usm.edu/fac_pubs/4499