Aerospace engineers encounter vortex methods as undergraduates. The famous thin airfoil theory is a continuous vortex sheet. The famous XFOIL is a panel method with an IBL solver for viscous effects.

Q: Can a simple discrete vortex method capture thickness?

A: Yes, but I would recommend a linear vortex method instead.

NACA 4412 at 10 degrees: 200 Elements

NACA 4412 at 10 degrees: 16 Elements

The source code and executable are available here.

The visualization is a pure Fortran library exporting to scalable vector graphics (.svg).