MBHB orbital decay results of the single isolated disc setup simulated using RAMCOAL at 10, 50, and 100 pc resolution together with the semi-analytic counterpart without accretion and feedback (with colors as indicated in the top panel). Three runs with different star-formation random seeds in the galaxy were performed at each resolution to gauge the effect of stochasticity in the galactic environment on the MBHB orbital decay. The top panel shows the MBH separation time evolution. The second, third, and fourth panels show the stellar, DM, and gas density, respectively, used to calculate the DF on the secondary MBH. The vertical dotted lines in each panel indicate when the MBHB evolution is handed over to RAMCOAL from RAMSES at the boundary of the resolution sphere. The black crosses indicate the triggering of subgrid density profiles. The black dots indicate the transition from stage 1 to stage 2 in RAMCOAL.