Environmental Engineering Reference
In-Depth Information
Simulation time and the need for
rapid methods
failure changes with time as a result of natural
deterioration and maintenance operations. Proba-
bilistic risk-based methods, where risk is under-
stood as combining probability and consequence,
therefore need to consider a number of inundation
scenarios that can reach thousands to hundreds
of thousands. Traditional mesh-based numerical
techniques are inapplicable, particularly when
such risk-based methods are applied to country-
wide scales. This has recently motivated research
into so-called 'rapid flood spreading' methods
(Gouldby et al. 2008), which in their initial form
simply consist in pre-processing Digital Elevation
Models to separatefloodplains into 'impact zones',
and establishing a volume-spreading rule based on
storage capacity within these impact zones and
ground elevations at the communication points.
For each scenario of a risk computation the 'rapid
flood spreading' calculation succeeds in achieving
run times several orders of magnitude shorter than
hydrodynamic time-step-based simulations. In
their present state these methods do not take into
account resistance and momentum effects that
may affect the final state of inundation, and do
not predict any time-varying flood depth or veloc-
ity outputs, which may eventually become desir-
able to include in risk computations.
In recent decades, efficiency in numerical model-
ling has been governed primarily by the exponen-
tial increase in computer power. The number of
transistors that can be placed inexpensively on
an integrated circuit has doubled approximately
every two years ('Moore's law', Moore 1965), and
this trend is continuing to be observed towards
2010. Other factors include progress in the design
of efficient numerical methods, although this
rarely leads to step changes in computation
efficiency, primarily because the Courant-
Friedrichs-Lewy-condition imposes a limit on the
size of usable time steps in explicit numerical
schemes. A similar, although less stringent, lim-
itation affects implicit schemes, in which the use
of excessively large time steps leads to unphysical
oscillatory solutions.
Recent research in the area of parallel proces-
sing should also be mentioned. This consists in
using simultaneously a cluster of computers or
a cluster of processors within a computer
(Hervouet 2007). The challenge is to divide nu-
merical algorithms into subalgorithms that are as
independent as possible from each other and be-
tween which the amount of information that is
transferred is limited. This has been implemented
in research codes (Kramer and Stelling 2006;
Hervouet 2007; Wright and Villanueva 2008) but
commercial applications do not yet exist.
However, the demand on computational effi-
ciency imposed by the need to simulate inunda-
tion modelling scenarios as part of risk-based
methods (Hall et al. 2003; Gouldby et al. 2008)
makes any advances permitted by the above or by
the use of unstructured or coarse meshes insuffi-
cient. Flooding can arise from different sources -
extreme tidal surges or fluvial flows, for example -
occurring on their own or in combination with
each other. For strategic planning purposes, time-
scales of a century or more are under consider-
ation, and uncertainties due to climate change
must be taken into account. Defences designed
tomitigate flood risk can fail, and failing processes
are poorly understood, while the probability of
Discretization of the physical space
One of the challenges of flood inundation model-
ling arises fromthe extreme non-uniformity in the
physical dimensions of the processes of interest.
European floodplains have typical dimensions
ranging from a few dozens of metres to a few
dozens of kilometres. Within these, natural land-
forms and made-made structures such as levees
and embankments, typically a fewmetres in trans-
verse dimensions, may strongly affect flow routes.
At the local scale, and primarily in the urban
environment, walls and other structures often
have a critical impact, and hedges and fences also
result in large head losses. For consistency, appro-
priate approaches should be applied tomodel these
obstacles if attention is otherwise paid to the
modelling of surface roughness.
