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combining two spherical sub-grids in such a way that their singularities are not close to their
own wet grid points. The first sub-grid, G, covering the Southern Hemisphere, the Indian
Ocean, and the Pacific Ocean up to the Bering Strait, is based on geographical spherical
coordinates. The second sub-grid, G', is associated with spherical coordinates having their
poles on the Equator. This second grid encompasses the Northern Hemisphere part of the
Atlantic together with the Arctic Ocean. The two sub-grids are connected to each other in the
equatorial Atlantic. With this technique, there is thus no singular point, neither in G, nor in G'
(Fig. 12).
Figure 12. Illustration of the two-grid system, with the connection line in the equatorial Atlantic
(courtesy Jacques Haus).
Instead of solving the equations of the model separately on the two sub-grids - with
appropriate matching of the fluxes across the connection line -, we consider the two spherical
coordinate systems as a single, orthogonal, curvilinear coordinate system. This way, the
computational domain does not have to be viewed as a set of two sub-domains. On the other
hand, however, the governing equations must be written - and solved - in a curvilinear
coordinate system, which is slightly more complicated.
The North Pole of G' is located on the geographical equator at longitude 9", 70°, i.e., in the
Indian Ocean (Deleersnijder et at., 1993). Let a, A and geographical longitude and latitude, respectively. If A' and
(Deleersnijder et at., 1993)
combining two spherical sub-grids in such a way that their singularities are not close to their
own wet grid points. The first sub-grid, G, covering the Southern Hemisphere, the Indian
Ocean, and the Pacific Ocean up to the Bering Strait, is based on geographical spherical
coordinates. The second sub-grid, G', is associated with spherical coordinates having their
poles on the Equator. This second grid encompasses the Northern Hemisphere part of the
Atlantic together with the Arctic Ocean. The two sub-grids are connected to each other in the
equatorial Atlantic. With this technique, there is thus no singular point, neither in G, nor in G'
(Fig. 12).
Figure 12. Illustration of the two-grid system, with the connection line in the equatorial Atlantic
(courtesy Jacques Haus).
Instead of solving the equations of the model separately on the two sub-grids - with
appropriate matching of the fluxes across the connection line -, we consider the two spherical
coordinate systems as a single, orthogonal, curvilinear coordinate system. This way, the
computational domain does not have to be viewed as a set of two sub-domains. On the other
hand, however, the governing equations must be written - and solved - in a curvilinear
coordinate system, which is slightly more complicated.
The North Pole of G' is located on the geographical equator at longitude 9", 70°, i.e., in the
Indian Ocean (Deleersnijder et at., 1993). Let a, A and geographical longitude and latitude, respectively. If A' and
(Deleersnijder et at., 1993)