Science Fair?
 

Ok, so I'm finishing up a 2d cfd code that can do Stokes' flow, and steady/transient Navier-Stokes. It uses the finite element method and uses .msh files from GMSH as input, so it can handle pretty much any (2D) geometry. Oh, and I can calculate the pressure drag (the other component of the drag I have yet to code in). If you want to learn more about the specifics of the method I'm using, it comes from here: http://ta.twi.tudelft.nl/users/vuik/.../fem_notes.pdf
(Not using penalty method or divergence-free basis functions because I don't think they'd work well with flows with non-zero divergence, see next paragraph)

The thing is that I've been working for a long time on this code, and I want to make a submission to the Siemens competition for high-school. The only problem is that I don't have any ideas for what I want the actual project to be. I thought about looking into quasi-3D methods (I already modified the code to handle non-zero divergence), but I'm open to pretty much any problem. I also thought about comparing types of lumped mass matrices for triangles -- you can't use the Newton-Cotes/Gauss-Lobato integration rules because the jacobian is zero at one vertex of the triangle, so you might end up with zeros on the diagonal.

So do any of you have a (2D) project idea for a high-schooler?