Number of GMRES iterations for different CFL_hydro and different preconditioning strategy (including no preconditioning) for the red giant (left panel) and the young Sun (right panel) models. The tolerance of the linear solver is η = 10^-4 and the maximum number of iterations is set to 1000. The vertical dashed lines denote the position of CFL_hydro = 1 (blue line), CFL_adv = 1 (green line), CFL_rad = 1 (red line). In the right panel, CFL_rad = 1 falls outside of the figure.