Application of the DuFort‐Frankel and Saul'ev methods with time splitting to the formulation of a three dimensional hydrodynamic sea model

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Abstract
A three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co‐ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort‐Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort‐Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.