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

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Ignacio Valcárcel LencinaTRITA LWR Masters ThesisFigure 23. 2D Geometry model.5.6 Bathymetry profile.In the two-dimensional model, it is necessary to definea function with two variables (x,y) to define thebathymetry. For the test case, the geometry andbathymetry illustrated in the figures below have beenimplemented. Since a source of strong non-linearitiesis the real bathymetry, a sin(x)cos(y) generated surfacehas been used for the test case. The function used issin(x)·cos(y)/10 , in order to compare with the 1Dmodel with an equivalent function.It defines a similar surface as the one used for the 1Dmodel with the function sin(x)/10, that is, a group ofsmall elevations of ±10 cm downstream of the dam.This kind of bathymetry defined analytically allows usto check its effect on the water surface easily, justchanging the denominator, for instance.Figure 25. View in perspective of the initial conditions andthe bathymetry.5.7 Initial value.The initial conditions are already well-known. Thelevel of water is 10 m high before the dam break and 3m downstream of the dam. The way to define it isexactly the same as it was done in the 1D model, thatis, z 0 = (10)*(x=50).Figure 26. The initial condition at t = 0.Figure 24. Layout of the bathymetry profile.5.8 Meshing.When trying to solve a problem that does notconverge, or having solved a problem where thesolution does not seem properly resolved, there isoften a need for re-solving the problem using a finermesh. In these situations it is sometimes easier torefine the existing mesh than to regenerate the meshfrom scratch using finer mesh settings. The mesh hasbeen refined two times to solve the model correctly.In 2D, the regular refinement method divides eachelement into four elements of the same shape. Thefirst mesh is composed by 496 elements, the secondhas 1984 elements (496x4) and the mesh used (showedin the figure below) is formed by 7936 elements(1984x4). Since Comsol Multiphysics remeshautomatically, the finest mesh that the computer isable to run has been selected.14
Comparison between 1D and 2D models to analyze the dam break waveMesh curvature factor 0.3Mesh curvature cut off 0.001Resolution of narrow regions 1Resolution of geometry 10x-direction scale factor 1.0y-direction scale factor 1.0Mesh geometry to levelSubdomainFigure 27. Mesh with 7936 elements.Figure 28. Mesh with 496 elements.The consequence of solving the model with a wrongmesh is the inaccurate definition of the whole model.The effect is shown in figure 29, where is present astrange appearance of the initial value. The number ofelements of this mesh has been 496 instead of 7936.In the ‘Mesh Statistics’ (table 5), there are somestatistical data for the current mesh such as thenumber of elements and the minimum element quality.Table 5. Mesh Statistics.Number of degrees of freedom 48171Number of boundary elements 184Number of elements 7936Minimum element quality 0.60365.9 Subdomain settings.The previous discourse about the 1D-subdomainsettings is analogous for the 2D model. The samegeneral equation has been adapted in this case, usingthe two-dimensional expressions, as we can see in thefollowing figures:∂ud a+ ∇ ⋅ Γ = F∂t⋅ (17)Figure 29. Mesh with 496 elementsFigure 30. The flux vector tab.Table 4. Mesh Parameters.ParameterValueMaximum element sizeMaximum element size scaling factor 1Element growth rate 1.315
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Comparison between 1D and 2D models to analyze the dam break

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