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

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Ignacio Valcárcel LencinaTRITA LWR Masters ThesisThe simulation clearly shows the influence of the bed’stopography on the elevation of the water surface.Comparing these results with those obtained from themodel with flat bottom topography, the influence ofthe topography is proved.Figure 17d. Water surface at t = 5.4 s. Model with flatbottom topography.The total computation time for this model has been 59s, eight seconds faster than the previous model;obviously the complexity of this model is different.Figure 17a. Water surface at t = 0 s. Model with flat bottomtopography.4. - VALIDATION OF TH E 1D MODELIn general, validation is the process of checking ifsomething satisfies a certain criterion. At this point, itis needed to check if the results are satisfactory or not.It will be done comparing the solution obtained withComsol Multiphysics (CM) with other solutions of thesame problem.The definition sketch of the model that we comparewith is the figure below:Figure 17b. Water surface at t = 2.7 s. Model with flatbottom topography.Figure 17c. Water surface at t = 4 s. Model with flat bottomtopography.Figure 18. Definition sketch of the model for the validation.A wide, horizontal, rectangular and frictionlesschannel is used to simulate the dam-break flow. Attime t = 0 + , the dam is removed instantly. The nexttwo figures below show that the most similar solutionof the model solved with CM is the analytical. In thissolution we observe that the wave front is almostvertical (both upstream and downstream of the dam),which is very close to our solution. The othersolutions are also similar. By comparison with the fivesolutions given by Rahman and Chaudhry (1997), weconclude that the code is satisfactory valid to solve the1D dam-break flow.The analytical dam break solution is given by Ritter in1892. This solution is:2 ⎛ x⎜ + c3 ⎝ t=0⎞⎟⎠u (13)12
Comparison between 1D and 2D models to analyze the dam break wave4 ⎛= ⎜c9g⎝0x ⎞− ⎟2t⎠2h (14)with c0 = g ⋅ h0(15)being h 0 the initial water depth in the reservoir and tthe time.Coriolis parameter takes into account the Corioliseffect caused by the rotation of the Earth. Theexpression to get f is:f = 2ω ⋅sinφ(16)Where ω is the angular velocity vector of the rotatingsystem and φ is the latitude. The assumed value for fhas been 2.4110 -5 . The other values are the same as inthe 1D model.Figure 21. The constants dialog box.Figure 19. Comparison of different solutions given by Rahmanand Chaudhry.5.4 Scalar expressionsIn this case, the same expressions as in the 1D modelhave been used, but obviously in two dimensions.Figure 22. The Scalar Expressions dialog box.Figure 20. Model solved with Comsol Multiphysics.5. - MO DEL L I N G THE 2D DAM-BREAKWAVE5.1 Assumptions.In this 2D model we accept the same assumptions asin the 1D model (section 3.1). The only difference tostand out is the bathymetry profile that will be seenfurther on in [5.6].5.2 Dependent variables.The dependent variables for the 2D model are z, zuand zv. Where z is the depth of water, zu and zv areunit discharges along the co-ordinate directions.5.5 Geometry.A rectangle is drawn to define the geometry of the 2Dmodel (figure 23). This is the domain where theequations are valid. The rectangle has dimensions100x50 m. The long side of the rectangle has the samelength as the line drawn for the 1D domain in order tocompare both models, one of the objectives of thisthesis. The first simulations were run with a 200 mdomain but the computational effort was too high forthe 2D model using such a dense mesh. As a matter offact, the dimensions of the domain are not soimportant because the whole model is defined exactlythe same. The maximum length that the computer wasable to run in 2D has been chosen, with the highernumber of elements in the mesh to be as accurate aspossible.5.3 Constants.The same constants seen previously in the 1D modelexcept the Coriolis parameter f have been used. The13
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Comparison between 1D and 2D models to analyze the dam break

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