Abstract: Today, many organisations rely on hydrodynamic modelling to assess the consequences of dam break failure on downstream populations and infrastructure. The availability of finite volume shock-capturing schemes and flexible mesh schematisations in widely used software platforms imply that dam break modelling projects will be carried out differently in the future: Finite volume based platforms allow widespread application of shock-capturing methods and flexible mesh platforms can represent features in the study area more realistically and are more flexible thanks to varying mesh resolutions. Furthermore, the recent adoption of Graphics Processing Unit (GPU) technology in mainstream scientific and engineering computing will also significantly decrease computation times at relatively low cost. This paper examines the application of finite volume, flexible mesh and GPU technologies to dam break modelling. One-dimensional (1D) modelling results are compared to those from two-dimensional (2D) finite difference and finite volume approaches. The results demonstrate that there are differences between modelling approaches and that the computational speeds of 2D simulations can be significantly reduced by the use of GPU processors.

1. 1 Dams and Water for the Future
Changes in dam break hydrodynamic modelling practice
S. Suter1
, G. Singh2
, and M. Britton3
1
DHI Water and Environment
50 Clarence Street
Sydney NSW 2000
2
State Water Corporation
55 Clarence Street
Sydney NSW 2000
3
DHI Water and Environment
12 Short Street
Southport QLD 4215
Abstract: Today, many organisations rely on hydrodynamic modelling to assess the consequences of dam
break failure on downstream populations and infrastructure. The availability of finite volume shock-
capturing schemes and flexible mesh schematisations in widely used software platforms imply that dam
break modelling projects will be carried out differently in the future: Finite volume based platforms allow
widespread application of shock-capturing methods and flexible mesh platforms can represent features in
the study area more realistically and are more flexible thanks to varying mesh resolutions. Furthermore,
the recent adoption of Graphics Processing Unit (GPU) technology in mainstream scientific and
engineering computing will also significantly decrease computation times at relatively low cost.
This paper examines the application of finite volume, flexible mesh and GPU technologies to dam break
modelling. One-dimensional (1D) modelling results are compared to those from two-dimensional (2D)
finite difference and finite volume approaches. The results demonstrate that there are differences between
modelling approaches and that the computational speeds of 2D simulations can be significantly reduced by
the use of GPU processors.
Keywords: Dam breach, flexible mesh, finite volume method, GPU
1 Introduction
Dam failure can cause catastrophic consequences on
downstream populations, property and infrastructure. The
most cause of dam failure is extreme inflow events which
exceed the spillway capacity. The assessment of risk
associated with dam failure is complex. It is important to
predict an accurate potential flooding extent and the time
available to evacuate people. This is normally achieved
by applying a hydraulic model that simulates the
development of the breach failure, the subsequent flow
through the breach and the flood propagation downstream
of the dam. Traditionally consequence assessment has
largely relied on numerical approaches originally
developed for natural floods or coastal hydrodynamics.
Engineers and hydrologists have generally not had access
to approaches more readily representing the sudden and
extreme changes encountered in dam break flows. While
some practitioners have applied advanced techniques to
dam break problems in the past, such investigations were
usually unable to be quickly applied to a large number of
scenarios, or to easily produce the range and extent of
output required for a comprehensive dam break failure
risk assessment.
Several technological developments mean that dam break
modelling projects will be carried out differently in the
future. Accurate modelling of a sudden shock-wave
caused by dam break failure requires fine spatial and
temporal resolution. The availability of finite volume
shock-capturing schemes and flexible mesh
schematisations in widely used software platforms will
see these progressively used as the standard approach for
dam break inundation modelling. These methods can
overcome the trade-off between accuracy of results and
the computational time. Finite volume based platforms
allow widespread application of shock-capturing methods
able to robustly model both subcritical and supercritical
flows, discontinuities such as hydraulic jumps and steep
topographies. Flexible mesh schematisation with
combined unstructured triangular and quadrangular grids
allows different spatial resolutions in the same model
domain and a smooth representation of geometries (such
as the developing dam breach profile) and boundaries in
the study area. The total number of grid elements can be
highly reduced compared to the traditional finite
difference method as smaller elements are applied only at
areas where greater detail is required.
Furthermore, the recent adaptation of Graphics Processing
Unit (GPU) technology in mainstream scientific and
engineering computing significantly decreases
computational times at relatively low cost and makes it
feasible to assess a broader range of dam failure scenarios
within project time frames.
This paper examines the application of finite volume,
flexible mesh and GPU technologies to dam break
modelling. It presents the results of a dam break
inundation analysis carried out using several different
hydraulic modelling and computational approaches.
Modelling results from one-dimensional (1D) and two-
dimensional (2D) approaches are compared. 2D
approaches include finite difference and finite volume
methods. Furthermore, the computational simulation
speeds using normal CPU and GPU processing are
compared.
This paper is based on the work done by Atiquzzaman et
al. (2011a & 2011b).
2 Application
2.1 Study site
The application of dam failure modelling is applied for a
dam for regulated river water supply with a sizeable
upstream catchment (Figure 1). The lake reservoir
upstream of the dam is usually filled by several rivers and

2. ANCOLD Proceedings of Technical Group 2
creeks. There is a spillway located around 1 km north-east
of the dam (Figure 2).
Figure 1 The dam
Figure 2 The spillway
2.2 Dam failure setup
The 1D and 2D dam failure models are developed
separately using MIKE 11 and MIKE FLOOD,
respectively. Both models use the same dam breach
parameters (Table 1). A random breaching width of 200
metres, a rectangular breaching section and a horizontal
bottom slope after the failure are assumed.
The models are run for a period of three days with the
dam failure starting two days after simulation start and the
breach developing over six hours. Filling of the dam is
achieved using a large design event inflow hydrograph.
Table 1 Dam breach parameters
Dam breach parameter Value
Dam height 76 m
Dam crest level 365 m AHD
Breach bottom level 315 m AHD
Failure method Overtopping
Breaching time 6 h
Breaching width 200 m
Dam failure in the 1D models (MIKE 11) is set up by
adding a dambreak structure to the model network at a
specific branch location. Dam geometry, head loss factors
and failure moment are defined. The breach commences
close in time to the point of crest overtopping and
develops to full width/depth over a period of 6 hours. The
breach development is defined by setting up a time series
file that specifies the breach level, width and slope over
the simulation period. Between the specified times the
breach parameters are linearly interpolated.
Two 1D models are set up, differing in their breach
calculation method. In the first model the flow through
the dam breach is described using the energy equation. In
the second model, the NWS DAMBRK dam-breach
method is used. This method uses a weir type equation to
determine flow through the breach (MIKE by DHI, 2014).
The dam failure in the 2D models (MIKE FLOOD) is
implemented by setting up a dynamic topography file.
This file contains the topography of the study area and
dam wall geometry at specific time steps, prior to and
after the breach formation. The topographic values are
linearly interpolated between these time steps.
The method describing this dynamic deformation is called
‘landslide’ in the grid finite difference model and is
described by Kofoed-Hansen et al. (2001). Its governing
equation includes interaction between deformation and
water, and the additional effect due to viscous and inertia
forces (Larsen and Tuncok 2009). An illustration of the
topography file (grid) used in the finite difference 2D
model at the dam site before and after the breach is
presented in Figure 3 and Figure 4 (note the angular
“stepped” edges of the defined breach).
Figure 3 Dam before the breach
In the finite volume 2D models (square mesh and flexible
mesh models), a similar method of deforming bathymetry
is used, except it is implemented as a “depth” change,
with a time varying map of depth changes to simulate the
dam wall lowering into the breach.

3. 3 Dams and Water for the Future
Figure 4 Dam after the breach
2.2 2D model schematisation
Three 2D models are set up:
• Grid model: This model uses a topologically square
network of lines (“grid”) to construct the discretisation of
the partial differential equations (PDEs). The numerical
solution used to solve the PDEs is the finite difference
method.
• Square mesh model: This model uses a mesh that is
made up of square elements. The finite volume method is
used as numerical solution for the PDEs.
• Flexible mesh model: This model uses a mesh that is
made up of elements with varying shapes (“flexible
mesh”). The finite volume method is used as numerical
solution for the PDEs.
The grid model and the square mesh model both use a
constant quadrangular element size over the entire model
domain. This is shown for the dam location in Figure 5.
The flexible mesh is made up of both triangular and
quadrangular elements with varying sizes. The elements
are smaller at areas where more detail is required such as
the dam crest and in areas where there are significant flow
changes. The elements are larger where less detail is
needed, such as the lake reservoir behind the dam and in
areas that do not get flooded. The mesh generally consists
of triangular elements; however, at the dam breach
location and the spillway outlet it is made up of
quadrangular elements allowing for element alignment
parallel to flow direction (Figure 6).
Note that the different colours on Figure 5 and Figure 6
represent different topographic values (red: high, blue:
low).
Figure 5 Square mesh at the dam breach location
Figure 6 Flexible mesh at the dam breach
A comparison between the element characteristics of the
different 2D models is provided in Table 2. It is shown
that even though there are areas of higher resolution in the
flexible mesh model (element length can be up to 3 times
smaller than in the grid model and square mesh model),
the total number of elements can be significantly reduced.
The reason for this is the relatively large lake reservoir
behind the dam that can be modelled with a coarse mesh
(element length up to 440 m). Hence, despite a lower
number of total elements in the flexible mesh model, there
is no loss of accuracy.
Table 2 Element characteristics for the 2D models
Grid model/
Square mesh
model
Flexible mesh
model
Number of
elements
371,882 66,539
Element length 20 m
6.6 m (min)
440.0 m (max)

4. ANCOLD Proceedings of Technical Group 4
2.3 GPU runs
For comparison purpose, the square mesh and flexible
mesh 2D models were run on both a 8-core CPU X5680
3.33 GHz processor and a NVIDIA GeForce GTX Titan
GPU processor. It should be noted that the 2D grid model
does not run on a GPU processor.
3 Results
An analysis of the outcomes of the different models was
done by comparing water level and discharge
hydrographs at the dam site.
A water level hydrograph was compared at a location
approximately 500 m upstream of the dam in the lake
reservoir (Figure 7). The results show very similar water
levels between the different models for the period before
the dam breaches. Once the water reaches the dam crest
elevation of 365 m AHD the dam starts to breach (time:
3/1/2010 16:30) and water is released from the lake
reservoir through the breach. For the period during and
after the dam breach, the 2D models typically drain more
quickly than the 1D models. This is due to cross-sectional
geometry defining the reservoir in the 1D model acting as
a “limiting section” once the reservoir level approaches
340 m AHD (see Figure 8).
Figure 7 Simulated reservoir water level upstream of
breach
Figure 8 1D model geometry at reservoir acting as a
limiting section for breach formation
The dam breach discharge hydrograph was compared for
the different models. The five models produced similar
results in terms of a triangular shaped hydrograph (Figure
9), with significant variations in peak and recession curve
behaviour. At the time the dam breach starts, the
discharge increases and reaches its maximum at the end
of the dam breach (time: 3/1/2010 22:30) in all the
models. However, the peak discharge in the three 2D
models is bounded by the two 1D model results, with the
energy equation 1D model providing a lower bound and
the NWS DAMBRK 1D model providing an upper bound
approximately 15% higher than the energy equation 1D
model. The peak discharges from the 2D models are
similar and trend towards the upper end of the range of
variability established by the two 1D solutions (Table 3).
After the peak is reached the discharge through the breach
decreases more slowly than in the 1D models, consistent
with a lower reservoir level.
Figure 9 Simulated breach discharge hydrograph
Table 3 Peak discharge comparison
Model Peak discharge (m3/s)
1D (energy eq.) 80,336
1D (NWS eq.) 91,823
2D grid 87,253
2D square mesh 86,854
2D flexible mesh 88,684
The elapsed computational times to simulate the 2D
model runs on the standard 8-core CPU and GPU
processor were compared (Table 4). On the CPU,
comparing a finite difference (grid) and finite volume
(square mesh) model with the same number of
cells/elements, the explicit finite volume code is much
slower. This speed difference between the explicit and
implicit code in MIKE21 has always been recognised, and
users of the finite volume code achieve computational
efficiency through parallelisation across multiple cores
(up to 64 cores on standard Windows machines and up to
1000 or more cores in the Linux based HPC (High
Performance Computing) environment.
320
325
330
335
340
345
350
355
360
365
370
Waterlevel(mAHD)
Time
1D model (energy
eq.)
1D model (NWS
eq.)
2D grid model
2D square mesh
model
2D flexible mesh
model
Dam
breach
start
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
Discharge(m3/s)
Time
1D model
(energy eq.)
1D model
(NWS eq.)
2D grid model
2D square
mesh model
2D flexible
mesh model

5. 5 Dams and Water for the Future
Table 4 Comparison of computational time between
CPU and GPU simulations
Model
Computational time (h) Factor of
speed
increaseCPU GPU
2D grid 21.3 - -
2D square mesh 148.6 21.5 7
2D flexible mesh 47.3 6.6 7
The GPU processor results in a speed increase of a factor
of 7 for the finite volume code compared to the CPU
simulation. This performance improvement is very
significant, since it comes from a relatively small
investment in hardware (high performance gaming cards
retail for between $400 and $1000) compared to the more
substantial investment required in multiple CPU
processors in either the Windows or Linux environment.
4 Conclusions
A dam breach analysis has been demonstrated using both
1D and 2D modelling techniques. The dam breach was
simulated in MIKE 11 (1D) and MIKE FLOOD (2D)
using the same dam breach parameters. Two 1D models
were set up differing in their breach calculation method.
Three 2D models were set up differing in their underlying
discretisation of the PDEs. The results showed that the 2D
model configurations tested produced similar results in
terms of shape of water levels and discharge hydrographs.
However, the detailed modelling of the dynamic flow
field in and around the breach in the 2D models showed
breach hydrograph peak flow estimates can yield quite
different answers to the 1D solution (up to 10% higher
compared to the energy equation 1D model). The 1D
solution is a more simple application of the energy and
weir equations (no roughness) across the breach and it is
therefore likely to produce different results than the
dynamic ‘landslide’ solution. Differences between the 2D
models can be due to different mesh/grid set ups, with
flexible mesh techniques being able to better represent
complex geometries and varying resolutions. The flexible
mesh approach provides the ability to vary the mesh size
appropriate to the modelling area to balance
computational speed against the accuracy.
Furthermore, it could be shown that the use of GPU
processors for dam breach and flood modelling can
significantly decrease the computational time of the
model runs. Hence, the use of GPU in dambreak
hydrodynamic modelling practice makes it feasible to
assess a broader range of dam failure scenarios within
project timeframes.
5 Acknowledgements
We thank State Water Corporation for supporting the
research through provision of LiDAR data, 1D dambreak
model files and previous modelling results.
6 References
Atiquzzaman, M.; Britton, M.; Singh, G. 2011a. Dam
Breaching Analysis using 2D Modelling Approach. Paper
presented at the IAH Conference, Brisbane.
Attiqussaman, M.; Britton, M.; Singh, G. 2011b.
Alternative Modelling Approach for Dam Break Analysis.
Paper presented at the FMA Conference, Tamworth.
Kofoed-Hansen, H.; Gimemez, E.C.; Kronborg, P. 2001.
Modelling of landslide-generated waves in MIKE 21.
Paper presented at the 4th
DHI Software Conference,
Denmark.
Larsen, P. T.; Tuncok, I. K. 2009. A new approach to the
analysis of dam degradation. Paper presented at the
Second National Symposium on Dam Safety, Turkey.
MIKE by DHI. 2014. MIKE 11 – A Modelling System
for Rivers and Channels (Reference Manual).