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Parallel Algorithms and Numerical Modeling of Bays, Estuaries and Oceans

Mónica L. Martínez

Presented at the 1997 CRPC Annual Meeting Poster Session

Simulation of shallow water systems can serve numerous purposes. First, it can serve as means for modeling tidal fluctuations for those interested in capturing tidal energy for commercial purposes. Second, these simulations can be used to compute tidal ranges and surges such as tsunamis and hurricanes caused by extreme earthquake and storm events. This information can be used in the development planning of coastal areas.

Finally, the shallow water hydrodynamic model can be coupled to a transport model in considering flow and transport phenomenon, thus making it possible to study remediation options for polluted bays and estuaries, to predict the impact of commercial projects on fisheries, to model freshwater-saltwater interactions, and to study allocation of allowable discharges by municipalities and by industry in meeting water quality controls.

We will present error estimates and parallelization algorithms (including a decomposition strategy based on a Hilbert Space Filling Curve) for a finite element model, ADCIRC, of the shallow water equations based on a generalized wave formulation of the continuity equation.

We will also present a projection method to improve mass conservation for any given velocity field. As an example, the velocity field obtained from ADCIRC will be post-processed and the results will be discussed.

We will also present a new numerical method based on a higher-order Godunov (HOG) approach that is conservative, stable, formally second order accurate and produces no numerical oscillations. This method gives as good numerical results as does the ADCIRC simulator, but with the additional application to supercritical flow.