See for instance: How to choose the optimal solver for a PDE problem? - #2 by nate
or for even more details: KSP: Linear System Solvers — PETSc v3.17.1-435-gd0fabe2265 documentation
I would also suggest to compute the Reynolds number of your problem, as described in 4.2 of: Advanced partial differential equation models | SpringerLink
and consider:
A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier–Stokes equations - ScienceDirect
and the tutorial I posted in the previous post, that uses a slightly more advanced splitting scheme.