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# Example 1

The transition of mesh density
The example is the problem of flood analysis in the city. The boundaries are shown in Figure 1. The 25 squares inside represent the building. The mesh size on the internal boundaries should be smaller than on the external boundary. Figure 1. The geometry
The mesh size on the internal boundaries is specified 30m and 100m on the external boundary. The generated mesh is shown in Figure 2(a). The mesh near internal boundaries is magnified and shown in Figure 2(b). The mesh size ratio of external and internal boundaries reaches to 3.3. The total 18229 elements are generated, in which the maximum internal angle is 156.40 degree and minimum internal angle is 40.40. The number of elements whose internal angle greater than 150 degree or less than 30 degree is 3. (a) (b)
Figure 2. The mesh
The mesh size on the internal boundaries is specified 30m and 200m on the external boundary. The generated mesh is shown in Figure 3(a). The mesh near internal boundaries is magnified and shown in Figure 3(b). The mesh size ratio of external and internal boundaries reaches to 6.7. The total 8549 elements are generated, in which the maximum internal angle is 153.33 degree and minimum internal angle is 35.06. The number of elements whose internal angle greater than 150 degree or less than 30 degree is 1. (a) (b)
Figure 3. The mesh
The mesh size on the internal boundaries is specified 30m and 300m on the external boundary. The generated mesh is shown in Figure 4(a). The mesh near internal boundaries is magnified and shown in Figure 4(b). The mesh size ratio of external and internal boundaries reaches to 10. The total 7383 elements are generated, in which the maximum internal angle is 158.85 degree and minimum internal angle is 21.63. The number of elements whose internal angle greater than 150 degree or less than 30 degree is 10. (a) (b)
Figure 4. The mesh