M.M.
Laguzzi, Guus S.Stelling, Karin de Brujin
WL
| Delft Hydraulics, Delft, The Netherlands
Delft
Hydraulics, Technical University of Delft
P.O.Box
177, 2600 MH Delft
The
Netherlands
Telephone:
+31-15-2858585, Telefax: +31-15-2858582
Email:
Marcela.Laguzzi@wldelft.nl, info@wldelft.nl, DelftFLS.info@wldelft.nl
Internet
site: www.wldelft.nl
Abstract:
The Delft Hydraulics’ package Delft-FLS is
specially suited to simulate two dimensional dynamic flow over initially dry
land, as well as flooding and drying processes on every kind of geometry, in
lowland and mountain areas. These
features have been incorporated into a new flooding module known as “Overland
Flow Module” within Delft Hydraulics’ one dimensional system Sobek, giving
birth to the package Sobek-Channel & Overland Flow also known as Delft-1D2D
Flooding System.
One or more two dimensional domains can be added to a 1D network (or the
other way around). The 1D and 2D domains are automatically coupled at the 1D
calculation points whenever they overlap each other. The 1D channel network and
the 2D rectangular grid hydrodynamics are solved simultaneously using a robust
finite difference scheme (Delft’s scheme) and the Conjugated Gradients method.
The Delft scheme is able to tackle steep fronts, sub-critical and supercritical
flow. Two dimensional domains can be nested, providing a refining of the grid at
the desired locations. Dam-break/dike breaks can easily be simulated using,
among other possibilities, the controlled structures from the 1D system.
This approach speeds computations, while modelling in detail where
needed. The user friendly interface
allows the simultaneous observation of 1D and 2D results.
This system facilitates the study of flood events on natural river
basins, polders, channel-networked regions, urban areas and coastal areas.
Keywords: flooding simulation, one and two dimensional hydrodynamic modelling, evacuation, risk, damage, landscape planning
In 1998, Delft
Hydraulics (with the financial support of the Ministry of Public Works of The
Netherlands), started a research to assess the possibility of fully coupling one
dimensional and two dimensional models for flooding simulation purposes.
At that moment
Delft Hydraulics already had two powerful systems: Sobek and Delft-FLS. Delft-FLS
is specially suited to simulate the two dimensional dynamic behaviour of
overland flow over initially dry land, the influence of existing or future
infrastructure on the flow pattern, as
well as flooding and drying processes on every kind of geometry, in lowland and
mountain areas. Delft-FLS is based on the finite differences method applied to a
rectangular grid
SOBEK (Rural
& Urban ) is a complete
package formed by flexible modules suited to model
typical one dimensional channel / river and urban drainage / sewerage
problems (hydrodynamics and water quality simulation; on-line coupling with
hydrological and structures control modules).
Both packages
use the same very robust numerical scheme, known as the Delft or Stelling scheme
(see Stelling et al., 1998), which makes possible the simulation of both
supercritical and sub-critical flow, as well as flooding and drying without the
use special procedures.
After many
trials it was decided that the most efficient way to couple the existing one-
and two dimensional models was to built a two dimensional module in the existing
1D Sobek program, making use of its existing geographically oriented user
interface.
When applying
the Delft-FLS finite differences model, the area under study is schematised
within a grid composed of square cells. The two-dimensional shallow water
equations are applied at each cell: water levels and water depths are computed
at the centre of the cell using the mass conservation equation. The interchange
of water between the cells is solved using the momentum equations in the u and v
direction.
Sobek solves the
one-dimensional (De Saint Venant) flow equations using an staggered grid: the
mass conservation equation is applied at the calculation and connection points
(1D nodes), and the momentum equation is solved at the reaches between two
calculation/ connection points.
In order to make
one system of both models, the following actions were undertaken:
A two
dimensional cell is replaced by a 2D water level (depth) node plus four
pseudo-branches (see Figure 1).
Fig.1 Coupling of 1D channels with 2D cells (h: water level, u, v: velocities in x and y direction, dX: grid size, Q: discharge in 1D branch)
For example, the
cell 21 in Figure 1 is connected to cell 22 by means of a “2D-u type”
branch. To this branch applies the
2D-momentum equation in the “u” (x) direction; the width of the branch is
the width of the cell; the bed level and slope of the branch is determined by
the ground levels of cells 21 and 22; the convective term (v 
u/
x)
is solved using a weighted average of the neighbouring “v” velocities
The 2D
“waterlevel” node is fully integrated with the 1D node. Both nodes are
“numerically” (not physically) at the same place. Only one mass conservation
equation is solved at the 1D2D node. The
profile is formed by the 1D channel profile extended with the cell storage area.
The user has two options at this point: dike off or on (see Figure 2).
When there are no levees along the channel and/ or the profile higher levels are
not well known, then the user may choose the option off: then the 2D cell is
flooded as soon as the water level in the channel reaches the 2D cell ground
level.
Fig.2 Connection 1D2D water level node: option dike on or off
If
the profile has levees, the user may choose to consider them as such (option
‘on’): in this case water will flow into the 2D cell only when the water
level is higher than the top level of the profile (levees). In this case, the
ground level of the corresponding cell is automatically elevated, therefore
acting simultaneously as a barrier for eventual flooding water coming from
somewhere else.
In this way, the
2D schematisation has been transformed into “1D” type elements: branches and
nodes. This whole system can now be solved simultaneously by the same
computational core. The whole set of equations is solved using an enhanced
solver based on the combined application of variable elimination and the
Conjugated Gradients solving method (Stelling et. al, 1998). Eventually, the
same set of equations could be solved using the alternated directions implicit
method.
The
system allows the coupling of one or more 2D grid areas to an existing 1D
network. Similarly it is possible
to add a 1D network to an existing 2D model. Figure 3 shows the 1D
Sobek model of East-Groningen, The Netherlands, which has been
extended with the 2D area of Tussenklappenpolder (note as well the
channel network inside the 2D area). The same figure shows the results of the
simulation of the flooding caused by the dike break of November 1998. The dike
breach was intentionally started to avoid flooding in neighbouring cities.
Fig.3 1D&2D model of East-Groningen and the Tussenklappenpolder, flood November 1998, NL.
Two dimensional grids can be nested and / or overlap (the different domains are automatically linked to each other using the same kind of “1D” type connections). For example, given a rough grid covering a large area, the user may want to have more detail at certain places. Figure 4 shows three fine grids nested within a courser grid used to model the Liri River at Sora, Italy.
Fig.4 1D&2D model of the Liri River, at Sora, Italy (source model: Beta Studio, Italy). User Interface showing flood progression
Dike / dam
breaks can be simulated using 2D or 1D elements.
The breach evolution can be given as an input, or the user may choose to
use a simple dike-break formula embedded in an ad-hoc dike/dam break node.
Boundary conditions are applicable to the 1D elements and 2D grids. Line
boundaries along a 2D domain, such as tidal boundaries, are also possible.
All input and
output are managed through the Sobek- geographically oriented user interface.
The original UI has been enhanced in order to show 2D animation files
together with 1D results on line.
The performance
of the system is very satisfactory. It
performs better than pure 2D models, specially in those cases where pure
2D-models have to use very fine grids in order to describe the flow in streams
and channels properly. This 1D2D
system allows a very good description of the channel flow in 1D elements while
using a coarser grid for the two dimensional domain. The system is very stable
and in general it is faster than pure 2D hydrodynamic models (with the exception
of Delft-FLS, when making computations on very large grids).
The results
(water levels, water depths, velocities, moment of flooding, flood duration,
etc.) generated by the system are automatically stored in ASCII files compatible
with any GIS system. The system also produces animation files which show the
flooding progression.
These output
files can be used later on to compute damage and the number of victims caused by
a flooding and the risk. The output is extremely suitable to support the
preparation of evacuation plans. Additionally, the system can be used to prepare
/ evaluate infrastructure, landscape and urban development plans, under
different scenarios.
The system is
used, among other applications, by the Dutch Flood Information System (HIS) of
the Dutch Ministry of Public Works an Provincial partners.
The system is operated by local authorities in charge of taking action
during eventual flooding.
This innovative
and robust tool allows the simultaneous solution of one dimensional and two
dimensional schematisations. It is also a very flexible system, which allows the
user to extend or change the model schematisation at any time by adding 1D
elements, networks, 2D domains or nested grids.
This approach
speeds computations, while modelling in detail where needed.
This system facilitates the study of flood events on natural river
basins, polders , channel-networked regions, coastal zones and urban areas due
to combinations of causes such as natural discharges, extreme rainfall, high sea
levels or failure of the flood defence system.