The MELCOR and CORQUENCH codes are used for simulations of the late phase of a postulated total SBO at KWU KONVOI PWR reactor. The base line SBO sequence without any mitigation and some of its variants are simulated in detail with MELCOR, selected cases up to 10 days of the accident progression. The ex-vessel phases of these scenarios, with long-term molten core-concrete interactions (MCCI), are recalculated also with the specialized code CORQUENCH. The AM counter measures after the reactor pressure vessel failure, typically flooding of the melt by water from the top at different times, are taken into account. The incentive for the work was to investigate the retention of corium materials, which were subject to MCCI, for this particular type of containment. At the same time, the detailed analysis is performed of the effect of different models employed for the description of heat transfer at the melt-concrete interface (ablation modeling) and of the effect of the "coolability" models. The results of the calculations indicate that this type of the KONVOI containment is relatively resistant to challenges by the late-phase accident progression. The incorporation of the CORQUENCH coolability models into MELCOR/CORCON, where it is missing, should be of primary interest. The model of the heat conduction into concrete behind the ablation front could also be useful. The overall impact of this modeling option -which is available in CORQUENCH and not available in MELCOR- on the maximum ablation depth seems to be relatively high under conditions pertaining to our accident simulations.