Environmental Engineering Reference
In-Depth Information
watersheds, of the soil, of terrestrial or aquatic sediments, of aquifers, and of parts
of streams, and so forth. There are models of technical devices for environmental
purposes, in addition. Experimental set-ups in laboratories are simulated in order
to understand relevant processes.
The methods presented in this topic are deterministic, throughout. A search for
any statistics would be in vain. The description of processes is translated into
mathematical terms. Often the approach leads to differential equations, which are
conditions concerning the change of a variable, like concentration or population
density, in space and time. Nowadays the solution of such equations is not as
tedious as in former times. Using core MATLAB
®
, problems in 0 and 1 space
dimensions can be solved comfortably. Core MATLAB
is also convenient for
solving 2 and 3-dimensional problems with analytical solutions. For more complex
modeling in more than one dimension, toolboxes, especially the MATLAB
®
partial
®
differential toolbox, can be recommended.
The aim of the topic is to introduce basic concepts of environmental modeling.
Starting from basic concepts the problems are transformed into mathematical
formulations. Strategies for the solution of the mathematical problems on the com-
puter are outlined. The main aim of the topic is to communicate the entire path of such
a modeling approach. At some points algorithmic details will be omitted for the
general aim. Who is interested strictly in computer algorithms, will be better served
with a topic on numerics, applied mathematics or computational methods. It is
important that the modeler has a basic understanding of the underlying numerics.
There is no need, however, to dive so deep into the algorithms that one would be able
to program them oneself. In fact, it is an advantage of the chosen software that
modeling tasks, which could be handled only by people with profound programming
knowledge and skills, become now available to a wider audience.
Who is addressed? In a broader sense everyone is addressed, who is dealing with
or is interested in the simulation of environmental systems on a computer. In
a considerable part of the topic concepts of environmental modeling are introduced,
starting from basic principles, tackling differential equations and numerical
solutions. In another similarly big part of the topic special implementations are
introduced and described. If someone is very familiar with another mathematical
software, the topic may be of help too, as most of the described models can also be
realized using other maths computer programs.
There are several good and excellent topics on environmental modeling and on
MATLAB
. Richter (
1985
) deals with ecological systems and with time
dependencies (but no space dependencies), as well as Deaton and Winebrake
(
1999
) using STELLA
®
.
1
Shampine et al
.
(
2003
) also present MATLAB
®
modeling of ordinary differential equations; concerning applications they do not
address environmental modeling particularly; concerning methods, they do not
address partial differential equations. Gander and Hrebicek (
1997
) offer little to
®
1
See:
http://www.iseesystems.com/
.
