Various reactor concepts and technologies have been devised and evaluated to ensure the integrity of the core and the containment under a prolonged station blackout. After the successful validation of the passive auxiliary feedwater system (PAFS) of Advanced Power Reactor Plus (APR+), Korea is considering an improved APR+ with a passive containment cooling system (PCCS). In a previous paper, we suggested a PCCS design based on APR+ and performed a scoping analysis. We performed a MARS simulation for the thermal hydraulic evaluation of the system behavior, including natural circulation through the Passive Condensation Cooling Tank (PCCT) water pool and inside PCCS tubes as well as steam-air mixture condensation inside the containment. Through a simulation using the MARS system code, we investigated the effect of air holdup tanks (AHTs) on reduction of the air fraction in the containment, the effects of several steam-air mixture condensation models, the role of heat structures, and the flow instability inside the PCCS tubes. We found that the presence of AHT reduced the number of required PCCS tubes by more than half and the heat resistance of the steam-air mixture side is dominant in terms of governing the overall performance of PCCS. The embedded MARS condensation model and Uchida's correlation gave lower heat transfer coefficients than Dehbi's correlation, and heat structures removed more decay heat than PCCS tubes. Finally, intense flow instability inside the PCCS tubes was observed and was mitigated by placing orifice plates at the inlet of the PCCS tubes, increasing the height of the return nozzle, or increasing the tube angle.