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I'm trying to understand and implement panel methods for a two-dimensional airfoil. I haven't found yet a very detailed explanation on how to implement it, and there are some things I don't' still understand. Here it is how I would implement it, I know it is only one of many possible implementations, please let me know if it's correct and if it would work. I need just to compute the velocity field data of an airfoil in a flow, so I think I can use only vortices, without the need of sources, sinks and doublets. I describe the airfoil as a set of panels; then I place a vortex of unknown strength in the center of each panel. Then I create a system of equations to obtain the unknown strengths. I have to impose that the velocity field created by every vortex plus the flow has a zero component perpendicular to every panel, calculated at the center of the panel. Now I still need an extra condition, the Kutta condition, that states that the velocities above and below the trailing edge must be the same. So i obtain the unknown strengths by solving the system. But I have some doubts on the Kutta condition. Can I implement this condition just by imposing that the velocities are the same in the two control points that are the closest to the trailing edge?
And is it necessary to impose that the vortices in the lower airfoil edge rotate counterclockwise and those on the upper edge rotate clockwise, or it just results automatically from the solution of the system? Thank you.

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I had worked on this problem and prepared a short report which might answer some of your questions. In chapter 1, both lifting and non-lifting configurations are described in the context of cylinder and an airfoil. Here is the link to the report: https://www.dropbox.com/s/zqiawtqrfapgbmf/report.pdf .

Eq. (1.26) needs to be implemented to ensure the boundary condition for no-penetration condition and for the Kutta condition, based on Eq. (1.27), you need to add another equation to enforce it. Hope you find it useful.

For implementing the Kutta condition, you may also refer slide 25-29 from this presentation: http://www.ltas-aea.ulg.ac.be/cms/uploads/Aerodynamics04.pdf.

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A very good start is the book: Low-Speed Aerodynamics by Joseph Katz and Allen Plotkin.

It describes a variety of panel methods for airfoils and wings, and, best of all, it includes source code.

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