Hammer projections displaying the time and surface integrated radial mass flux on a sphere of R_shell = 30 AU for runs R1 (left) and R2 (right), displaying both the inflow (top colorbar) and outflow (bottom colorbar) of material throughout the simulation’s duration post-sink formation (t_f), computed by integrating Eq. (1) in time. The lime colored contour delimitates the transition from positive to negative values.