Mass conservation for ɛ_int = 0.9. The time derivative of Σ remains perfectly constant and equal to zero inside the cavity and only becomes moderately negative at the cavity edge R = 10. This suggests that the simulation indeed reaches a steady state for radii up to ≈8. The mass conservation is also correctly recovered. The three lines do not add up to zero because we used a moving average for better visibility, and the quantities are time-averaged on a sample selection of output flies that do not contain all the time steps computed by the code.