Environmental Engineering Reference
In-Depth Information
Similarly, Urich et al. (2010) investigated the generation of virtual sewer systems using the
agent based modelling approach. In this approach virtual combined sewer system are
generated on the basis of virtual environment (digital elevation model, land use, population
density etc) provided by VIBe. The infrastructure generation module exports the urban
drainage system in the format used by SWMM for further simulations. Stochastic
investigations and benchmarking of combined sewer systems can further be conducted based
on the results of computer simulations and the layout properties of virtual sewer systems.
The synthetic networks generated in the field of river and drainage networks are mostly
configured as fractal tree or system of branches. Water distribution networks are more
frequently looped rather than branched, actually quite often a combination of lopes and
branches. This makes the application of concepts used for drainage networks rather limited.
The concepts of network generation based on graph theory initiated in mathematics and
computer science offer more similarities to the network configurations typical for water
distribution.
For instance, Rodionov and Choo (2004) present in their paper of computational mathematics
the set of algorithms for generating connected random graphs (RG) based on specified
limitations, such as given node connectivity or different probabilities of links existence. The
process of sequential growth starts by generating spanning trees and then allocating
remaining links. If node connectivity has achieved its maximum number of connections, free
links are not considered to connect to it any more. All nodes are grouped around one or
several centres with restriction of density with distance. The intersection of links may occur
and there is a limitation to work with gradual increase in complexity for the number of virtual
cases. This graph generation algorithms are mostly useful to create the Internet structures but
some of the aspects are also applicable in water distribution; for instance, the planarity, non
uniformity of distribution of node's coordinates, or limitation of maximum number of links
connected to a node.
4.2
GRAPH THEORY TERMINOLOGY AND APPLICATION
Water distribution networks consisting of nodes and links are in graph theory presented as
graphs composed of
vertices
and
edges
, respectively. A network is usually mapped as a
directed graph
(or
digraph
) with edges that have capacities (e.g. flow rates), and vertices that
have demands, pressures etc. In water networks, the flow is delivered from sources to sinks.
When the flow direction is not considered, the network is an
undirected
graph
.
Figure 4.4
Various types of graphs
Search WWH ::
Custom Search