Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 230

FIGURE 6.1 Example of a grid for a three-dimensional (3D) computation. Two vertical

domains are used. The upper domain uses a sigma coordinate. The lower one uses a Cartesian.

surface remains constant in each of them. The control volume that makes that
calculation simpler must have faces perpendicular to the reference axis. If rectangular
coordinates are used, the control volume generating the simpler discretization is a
parallelepiped. In the case of a large oceanic model, a suitable control volume will
have faces laying on meridians and parallels.
In depth-integrated models, also called two-dimensional or 2D horizontal mod-
els, the upper face of the control volume is the free surface and the lower face is
the bottom. In three-dimensional or 3D models, a control volume occupies only part
of the water column and its shape depends on the vertical coordinate used. In coastal
lagoons, Cartesian and sigma-type coordinates (or a combination of both) are the
most commonly used coordinates.
The ensemble of all control volumes forms the computational grid. In finite-
difference-type grids, control volumes are organized along spatial axes and a struc-
tured grid is obtained. In contrast, typical finite-element grids are nonstructured. The
latter are more difficult to define, but they are more flexible, thus allowing some
variability in the spatial resolution. Figure 6.1 shows an example of a very general
finite-difference-type grid using several discretizations in the vertical direction.
A system can be considered one-dimensional (1D) if properties change only
along one physical dimension. In this case, control volumes can be aligned along
the line of variation and one spatial coordinate is enough to describe their locations.
Properties are considered as being constants across control volume faces perpendic-
ular to that axis. Fluxes across the faces not perpendicular to that axis are null or
have no net resultant.

6.2.2 C V A

ONTROL OLUME PPROACH

Control volumes used in numerical models have the same meaning as the derivation
of the evolution equation in Chapter 3. A discretization is adequate if it generates a
simple calculation algorithm while maintaining the accuracy of the results. The