An accident in a nuclear power plant involving a reactor core meltdown could result in the instigation of molten corium, which is a mixture of nuclear fuel, claddings and structural components. In this paper, an enthalpy-porosity model is proposed to comprehensively analyze the ablation of concrete during the molten corium and concrete interaction process. The developed numerical model is an extension of the enthalpy-porosity model and is termed the CCEPM. The developed CCEPM computational fluid dynamics model can predict natural convection, melting and solidification. The developed model simplifies the complex phenomena of concrete ablation and melting by incorporating the multiregional approach. The model was implemented in OpenFOAM by developing a new solver that couples buoyant-driven natural convection and conjugate heat transfer solvers. The thermal modeling and heat transfer capabilities of the developed solver were verified against experimental data sets. Additionally, the effects of various boundary conditions, concrete thermal conductivities and decay heat intensities were analyzed to study their impacts on concrete ablation. We observed significant low concrete ablation and controlled temperature and velocity fields for the water-cooled boundary condition. Accordingly, the ablation of concrete decreased by 17% by imposing the water-cooled boundary condition. Similarly, when the thermal conductivity of concrete was decreased to 0.43 and 0.13 W/m.K, the ablation of the concrete decreased by 38% and 75%, respectively. Furthermore, early cooling of molten corium to decrease the decay heat was found to be an effective strategy for successfully mitigating concrete ablation by 20%.