Turbine solver still isn't right

[jwallwork23]

While #36 re-enables the turbines in the turbine example, there's still something not right because the optimisation progress is non-monotonic and the control turbine area occasionally goes to zero.

          Looks straightforward. Just one comment: when I tried to run `make test` the optimization failed on the 6th iteration with a `control_turbine` area of 0. From the .vtu files, it appears to be approaching the boundary of the domain.

Originally posted by @acse-ej321 in #36 (review)

[stephankramer]

Finding the same here as @acse-ej321 - also many similar failures at other low resolutions. I suspect this is just caused by being completely under-resolved: at n=2 (as in the test) the mesh resolution dx=50 whereas the turbine diameter is D=16! In my experience you need at least dx=D/4 to get sensible and robust optimisation results for position even using a quadrature degree of 10. It might be that previously the "automatic" quadrature degree gave a much higher degree - i.e. something's changed in Firedrake's automatic estimate - so that you could get away with some coarser resolution. Currently it seems firedrake produces a quadrature of only degree=8 for the bump(x1, y1)*dx integral.

[jwallwork23]

Finding the same here as @acse-ej321 - also many similar failures at other low resolutions. I suspect this is just caused by being completely under-resolved: at n=2 (as in the test) the mesh resolution dx=50 whereas the turbine diameter is D=16! In my experience you need at least dx=D/4 to get sensible and robust optimisation results for position even using a quadrature degree of 10. It might be that previously the "automatic" quadrature degree gave a much higher degree - i.e. something's changed in Firedrake's automatic estimate - so that you could get away with some coarser resolution. Currently it seems firedrake produces a quadrature of only degree=8 for the bump(x1, y1)*dx integral.

Good points, thanks @stephankramer. As mentioned on thetisproject/thetis#382, I've figured out how to set this example up with discrete turbines, so I'll rework the implementation here in the coming days.