Environmental Engineering Reference
In-Depth Information
The work of
validation
is the most challenging. As the result of such work it is
proven that a model is valid, i.e. behaves like the real system. The term usually is
restricted to a field site application, but it sometimes also refers to the fact that
a code can be applied for a certain type of applications. In the later case for each
application site-specific parameters have to be included. Connected to software
tools the term 'valid' remains slightly obscure as its concrete meaning is to be
specified for each application field. It has to be clarified, which aspects of the real
model should be represented by the model. As a model is not identical to the
represented real system, there are always real world aspects for which the model is
not sufficient.
The step concept, visualized in Fig.
2.1
and Fig.
2.2
, is less a work schedule than
a priority list. The mathematical formulation has to be based on a good conceptual
model. If the mathematical formulation is insufficient, good solution techniques
will not improve the model. One has to be sure that the solvers deliver accurate
results, before putting extensive efforts into post-processing.
2.3 Fundamental Laws
The mathematical analytical formulation is based on fundamental principles and on
empirical laws. From the former most important are the principles of conservation:
Mass conservation
Momentum conservation
Energy conservation
Total mass, momentum and energy are preserved. If there are losses or gains,
these are introduced in the conservation formulation as sources or sinks.
2.3.1 Conservation of Mass
The most nearby and most common application of the continuity equation is that for
mass. There are two types of mass conservation. One type is the mass conservation
of the medium, which can be solid, aqueous or gaseous. The mass is expressed in
terms of a density
with a physical unit [M/L
3
]. 'M' represents a mass unit and 'L'
a length unit. For example the density of fresh water at a temperature of 4
C and the
pressure of 101,325 Pa (1 atm) is 1,000 kg/m
3
.
The second formulation of mass conservation in a fluid concerns biogeochemical
species within a fluid. In that case the mass is expressed in terms of the concentra-
tion
c
. The continuity equation then is formulated in terms of the concentration
c
of
the species. The concentration also has the unit [M/L
3
] and measures the mass
within a volume of fluid. The content of chloride Cl
-
in seawater amounts to 19 g/l.
r
