Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 229

built on the same concepts. Its implementation requires the definition of at least one
control volume, the calculation of the fluxes across its boundary, and the calculation of
the source and sinks using values of the state variables inside the volume. The number
of dimensions of the model depends on the importance of relevant property gradients.
The simplest model is the “zero-dimensional” model. In this model, there is no
spatial variability, and only one control volume needs to be considered. At the other
extreme of complexity is the three-dimensional (3D) model, which is required when
properties vary along the three spatial dimensions. Whatever the number of its
dimensions, a model must include the following elements:

• Equations
• Numerical algorithm
• Computer code

The order of the items in this list can also be considered the order of their chrono-
logical development. Hydrodynamic equations are based on mass, momentum, and
energy conservation principles, which were presented in Chapter 3. These have been
known for more than 100 years. Actually, numerical algorithms used to solve hydro-
dynamic models were attempted even before the existence of computers. The analytical
equations and the numerical algorithms developed before the existence of computers
allowed the rapid development of modeling starting in the 1960s, when computers were
made available to a small scientific community. Since that time, models and the mod-
eling community have evolved exponentially. Modern integrated computer codes have
done more for interdisciplinarity than 100 years of pure field and laboratory work.
The number of implementations of a model to solve various problems increases
the knowledge of the range of validity of the model equations. The accuracy of the
numerical algorithm is better known and confidence in the results increases. At that
time, the major source of errors in the results is the existence of mistakes in the data
files. Once the model equations, algorithms, and results are validated, the next priority
is the development of a user-friendly graphical interface that simplifies the use of the
model by nonspecialists. This reduces the errors of input files and simplifies the checking
of those files. This chapter presents the concepts and methodologies used to build models
and to understand their functioning.

6.2 NUMERICAL DISCRETIZATION TECHNIQUES

Computers can solve only algebraic equations. Analytic equations, integral or dif-
ferential, must be discretized into algebraic forms. The procedure followed depends
on the form of the analytical equation to be solved. The control volume approach
is best for the integral form of evolution equations, while the Taylor series is best
suited for differential equations.

6.2.1 C G

OMPUTATIONAL RID

The calculation of fluxes across a control volume surface is simpler if the scalar
product of the velocity by the normal to each elementary area (face) composing that