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I have been struggling to find a mapping of points interior to a Joukowski airfoil onto the unit disk.

According to the Reiman Mapping Theorem, such map should exist since I am looking a a simply connected domain.

My first approach was to obviously work with the Inverse Joukowski Map, which maps the boundary of my airfoil region onto the unit circle. However, that has proven unsuccessful so far and I am wondering if anyone has some thoughts on this...

Thanks

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