Comparison between 1D and 2D models to analyze the dam break

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Ignacio Valcárcel LencinaTRITA LWR Masters Thesis7. - DISCUSSION AND CO MPARISON OFBOTH MO DEL S.The results show that the two modelling approachesare close to each other. The most importantparameters to analyze after a dam-break flood (interms of safety) are the maximum free surfaceelevation and the propagation time of the wave. In the1D approach, the maximum surface elevation is a fewcentimetres higher than the elevation obtained withthe 2D, as we see in figures 55 and 56. In these figures,the evolution of the water surface is shown starting att = 0 with steps of 0.1 up to 5.4. Every line representsevery time step. Both figures are practically equal. Themaximum surface elevation is around 6 meters high(with 10 m as initial level at the reservoir).The propagation time is exactly the same for bothmodels. The results show an average velocity of thewave of 33.3 km/h. The wave propagation on a wetbed is faster than on a dry bed. This study focusesonly on the wet case, but we have to take this fact intoconsideration in real applications where the wave goesthrough both wet and dry zones (depending on thereached depths). In addition, the friction coefficientbecomes unimportant in a wet bed case. This is due tothe fact that the depressions that are normally filled bythe flood wave as it passes by are now already full ofwater when the computation begins. In realapplications, the friction coefficient is much moreimportant, especially for the propagation times. Theinfluence of friction on the maximum free surface issmall, even if it is known that the lower the frictioncoefficient, the higher the elevations.This thesis analyses the dam-break wave from atheoretical point of view. A simple example of thecollapse of a water supply reservoir in a narrow valleyhas been used to demonstrate the capability of themodel. In real contexts, the differences between 1Dand 2D models are significant and nowadays they areknown. We have studied the dam-break problem witha generic tool, which is not adapted to solve realapplications on large domains. On the other hand wehave studied in depth the problem and we can ensurethe validity of the two-dimensional approach.Until recently it was considered that two-dimensionaltools could not be applied to large domains, forreasons of computer time and memory. Moreover, thetopographic data available from field survey, generallycross-section geometry profiles, were simple toassimilate into 1D models. However, 1D results mustbe carefully interpreted to work out the final twodimensionalmaps showing flooded areas and arrivaltimes, and this may introduce additional errors into theanalysis. Calibration is also easier in 2D becausephenomena such as the effect of bends or obstaclesare naturally reproduced, whereas they are artificiallytaken into account via empirical head loss correctionsin 1D.Figure 55. Cross section of the evolution of the water surfacewith the 1D approach.Figure 56. Cross section of the evolution of the water surfacewith the 2D approach.In terms of non-theoretical simulations, someconsulted papers conclude that the new twodimensionaltools obtain an improvement on onedimension when there are sharp bends in the river (thebends are not taken into account in 1D simulations)and are necessary in cases where the flood spreads in acoastal zone. They also improve predictions of thewave celerity. Two-dimensional simulations of floodwaves are already possible on domains with a length ofsome 10 s kilometers. Larger domains (100 to 400 km)are also within reach with supercomputers, or withparallel architectures.There are a lot of uncertainties in the modeling andespecially in the one-dimensional flow modeling wherethe user of the model can have a significant effect onthe results by selecting the locations of cross-sectionscarelessly. The debris flow, clogging of bridges andother structures and erosion of flooded areas alsocause uncertainties in the flood simulation and thoseuncertainties must be taken into account.In addition, there are several topics in dam breakhazard analysis that require additional research.According to the RESCDAM Project (2001), thefollowing topics are of primary importance:22
Comparison between 1D and 2D models to analyze the dam break wave• Determining a dam breach formation (flowhydrograph).• Determining roughness coefficients used inflow simulations.• The effect of debris flow and urban areas in adam-break hazard analysis.8.- CON CL USION.One of the main goals of this study was to show thecapacity of a general tool called Comsol Multiphysicsto deal with dam-break simulations. This capacity hasbeen proved even though it has been done using asimple and idealized case. In parallel with the rapiddevelopment of computer technology within the last20 years, dam break and flood simulations havestepped from the use of simplified models to onedimensionalchannel network models and finally toexpensive two-dimensional models. The trend is tominimize the expert work in favor of computerresources.The main improvement expected from a 2Dcomputation was in terms of the accuracy of thepredicted propagation times. After the comparisondone in this work we don’t see this improvementbecause the models used have been theoretical andwithout irregularities, it has not been a realisticapproach. The use of a 1D model needs a lot ofexperience since the cross-sections have to be put atthe right locations. The use of a 2D model is morestraightforward. However, the results of the 1Dapproach are actually considered good because theyare on the safe side and safety is the key concept inthese problems.The 1D approach is even recommended by somedepartments like the Spanish Ministry ofEnvironment, where in its “Technical guide for thedevelopment of emergency action plans for dams” we read: “Ingeneral, it is desirable to use 1D models because they aresufficiently accurate and the 2D models usually are complex tomodel and to get the basic data (topography, directionalroughness, etc.) and force us to assume additional simplificationsto take into account the second dimension.”Thinking in terms of implementation, it is clear thatthe 1D approach is valid because it is conservative andgood enough; however, actually it is possible to thinkabout more and more accurate 2D models, thanks tothe rapid development of the technology. Today’sstate of the art procedure is to develop complexterrain models and superimpose them with floodcomputation parameters.Although a general conclusion of this report could bethat it is necessary to decide between 1D and 2D, it isnot quite that simple. The use of one doesn’t excludethe other. In fact, it is desirable to take both of theminto consideration. The resources for the 1D approach(computers and software) are more accessible,therefore this approach is very useful to getconservative screenings at the beginning. If theresources and data are available, a 2D model isadvisable for all the reasons expounded previously. Inaddition, the results of the performed 1D model canbe a great help to predict the results in the 2D model.In practice, the implementation may be best achievedcombining 1D and 2D models. A framework for adam break analysis is summarized in the Appendix,where the current practice is presented according tothe ICOLD (International Commission On LargeDams) recommendations. As it can be seen in theAppendix, the analysis is based using 1D and 2Dmodels.Typically 1D models are based on finite differencemethods (FDM). Apart from the research, even thelargest energy companies achieve the dam break floodanalysis with this kind of one-dimensional approach. Itis faster, cheaper and the results are fully satisfactory.The dam break studies have been attempted with the1D approach in the past, actually the “1D+2D”approach is becoming more common, and in thefuture, when the resources are completely accessible,the 2D approach could be the primary way to achievethese analyses.23
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Comparison between 1D and 2D models to analyze the dam break

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