Handling shock with obstacle

[warisa-r]

• [x] Process the data from obstacles celltape files and make them work with the current detection pipeline
• [x] In visualize.jl create the heatmap of obstacle data
• [x] Change the constructor to not accept mach_to_ms anymore
• Add more models that can fit the shock discontinuity better
• [x] hline model
• [x] document the result and findings from obstacle cases

[warisa-r]

The problem with parametization is that it is continuous through out the curves meaning we cant combine lines and arc. Implementing some parameterization that allow combination of multiple shapes in the curve might be something worth considering

[warisa-r]

The current models are sufficient in dealing with the models and fine-tuning the parameters of DBSCAN can help filter out a lot of numerical artifacts around the sharp edges of the obstacle

[warisa-r]

What is also interesting is that initial_guess from interpolation doesn't affect the fitting algorithm in terms of fit quality (which is already pretty decent with random initial guess).

However, with an initial guess that is implemented with interpolation (for the parabola model, which is one of the costliest models to compute the initial guess for), the runtime increased drastically, and thus, it isn't a good idea for obstacle cases we got.

My analysis is that the grid data of the simulations are quite small, making the range of the parameters pretty limited and the randomized initial guess is good enough. (Though I still think that initial guesses are good idea for simulations with larger x_range and y_range, this shall be further discussed in other issues #8 )

[warisa-r]

Documented in the report.