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Shallow water equations are often solved on a Cartesian curvilinear grid. In this way, the computational efficiency can be optimised by prescribing a high resolution in the area of interest, in combination with a low resolution at a greater distance at open model boundaries. Also, the adverse effects of closed “staircase” boundaries may usually be avoided. When simulating flows in larger areas such as open oceans, the model can no longer be expressed in plane coordinates. For these kind of applications on the globe, rectilinear spherical (Lon, Lat) coordinates have frequently been applied in the past.
Obviously, the combination of curvilinear and spherical coordinates would greatly enhance the applicability of Deltares’ modelling system Delft3D. Also, the application of spherical coordinates as defined by the World Geodetic System (WGS84) reduces the number of coordinate transformations in areas that are covered by more than one local coordinate system. The application of the WGS84 coordinate system is further stimulated by worldwide availability of GPS. Interfacing with third-party models such as meteorological models would be facilitated. Both the computational and the operational efficiency of the Delft3D modelling system would be increased if spherical curvilinear coordinates were supported.
In the current project, shallow water equations have been derived for spherical curvilinear coordinates in order to investigate the feasibility of the application of these coordinates in the Delft3D-FLOW solver. It appears that the equations in spherical curvilinear coordinates are identical to those equations which had already been implemented for Cartesian curvilinear coordinates. This implies that the new functionality may be obtained through the modification of just a few subroutines that ensure the computing of metric components.
The equations for generating an orthogonal grid in spherical coordinates are also presented.
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