The use of computers to simulate ocean currents, sea level, and the distribution of marine properties has come into its own in the past 15 years. The field of hydro-dynamic modeling now includes a variety of approaches that are commonly employed in three-dimensional, Eulerian, open-ocean, and coastal modeling studies. The rapid evolution of computing has driven growth of the field of hydrodynamic modeling, which has been catalyzed by the sharing of most models as opensource software (i.e., those that are freely available for general scientific use, as opposed to codes that are proprietary or with restricted source code availability). While the basic equations which underlie numerical hydrodynamic models are universally known, there are a wide variety of methods used to solve the systems. These affect the structure of the discrete grids used for the computations.

The models can be classified by their grid methods: regular or irregular horizontal grids, and a variety of vertical discretization schemes. Models also differ through the approximations which are required to model irresolvable processes, such as turbulent motions and complex interactions with the atmosphere. A wide variety of modeling techniques are required to satisfy the diverse modeling applications, from shallow water estuaries and open-ocean circulation to integrated earth system modeling used for global climate studies.

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