Environmental Engineering Reference
In-Depth Information
Modelling
Step
Reality
Chemistry
Physics
Biology
...
Conceptual
Model
Mathematical
Analysis
Differential
Equation
Analytical
Solutions
Numerics
Solution
Numerical
Evaluation
Post
Processing
Visualisation
Model
Fig. 2.1 Modeling steps
At first a conceptual model has to be formulated. From the available scientific
and technical expertise and knowledge, as well as the experience with observations
of the system in question, a concept has to be set up. The concept involves all
processes, which could be relevant for the studied system. This first step is a
qualitative one, i.e. there are no numbers involved yet. Scientific or technical
expertise from the involved branches has to be included. In case of environmental
problems advice has to be obtained from several disciplines mostly: chemistry,
physics, biology, biochemistry, geology, biogeochemistry, ecology, hydrology,
hydraulics, or hydrogeology.
The next step is the formulation of the model in mathematical terms. Variables
and parameters as functions of time and space are related to each other by mathe-
matical expressions. Rearrangements and transformations of the expressions usu-
ally lead to the formulation of differential equations. Fundamental theoretical or
empirical laws and principles are combined to finally yield differential equations. In
the simplest case there is a single equation only, in general a system of equations
emerges. It can be
ordinary differential equations
, which have a single independent
