How pressure fields change around wing?
Take a look at https://www.sciencedirect.com/topics/engineering/angle-of-attack  and  https://www.grc.nasa.gov/WWW/K-12/WindTunnel/Activities/lift_formula.html. 
Lift graphs have a linear portion for small angle of attacks (and in 2D scenarios), but drag and airflow (laminar (non-shedding) vs. turbulent (shedding)) are both are non-linear, and both affect pressure and thus lift, and are important in real-life and 3D calculations.