Advection in spherical coordinates?
I've written a RANS code in spherical coordinates and I want to confirm whether it produces the correct convection by running only the convection and comparing it with the analytical solution. This appears to be the standard practice for Cartesian coordinates. However, for spherical coordinates I haven't been able to find an analytical solution to the equations as I don't think the solution will simply be (u-xt) as in the Cartesian case. If anyone's got any ideas or a way to solve the equations analytically it will be much appreciated.
The convection in spherical coordinates is given by
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