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Instability of HydPy-Musk-MCT for discontinuous cross-section profiles #172

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@tyralla

During the (nearly finished) implementation of WQ-Widths-Strickler, I encountered cases where the results of Musk-MCT are questionable. Musk-MCT cannot handle discontinuous relationships very well. Using WQ-Trapeze_Strickler instead of WQ-Widths-Strickler makes no difference. This is what the musk_mct_base_example results look like if I change the profile geometry as follows:

nmbtrapezes(3)
bottomwidths(15.0, 200.0, 0.0)
sideslopes(5.0, 10.0, 100.0)
Image

If I set the number of segments to four (as in the musk_mct_long_segments example), the small inaccuracies become more relevant:

Image

I have no time for deeper investigations at the moment, but I suspect this is not due to a bug, but rather a general limitation of the methodology. However, others have applied MCT on more complex geometries, so I am not sure here. One may have to put some effort into making the degree of discontinuity low enough using a smoothing technique or a similar approach (maybe just avoiding stacked trapezes with large bottom widths). If so, we should mention this in our documentation.

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