I recently started using FEniCS, and I want to set up and solve the classic fluid mechanics problem of creeping flow past a solid sphere, which has an analytical solution [http://web.mit.edu/1.63/www/Lec-notes/chap2_slow/2-5Stokes.pdf] for the pressure and velocity fields.
I am having trouble setting up the correct geometry for this problem. The way the problem is solved analytically is by using 2D spherical axisymmetric coordinates, involving r and \theta. The Laplacian for this case is different from the 2D cylindrical case (despite the latter being in terms of r and \theta) which is covered in the “Flow past a cylinder” example discussed in the tutorial [https://fenicsproject.org/pub/tutorial/pdf/fenics-tutorial-vol1.pdf].
Any help in getting started with the geometry setup is greatly appreciated.
Thank you, yes, I have looked at the problem. I am interested in flow around a sphere in 2D, and not flow around a cylinder. In my mind, the two need to be handled differently, because their Laplacians are different even though both use r and \theta coordinates.
I would be grateful for any help on handling 2D axisymmetric flow past a sphere.