Diagram illustrating the computation of the optimal time step of the hot gas phase (). The two horizontal dash lines materialise the maximum variation, p%. In the case shown here, the evolution of the hot gas phase is dominated by input flows: Ṁ_sh + Ṁ_wind>Ṁ_cool. The optimum time step for the hot-gas phase evolution is therefore computed assuming an increase in the galaxy ejecta rate (1 + p%)Ṁ_wind.