In the event of a core meltdown in a high-power reactor, the integrity of the reactor pressure vessel is presumably protected by severe accident mitigation systems such as in-vessel retention external reactor vessel cooling (IVRERVC). However, in the late phase of the accident, two possible locations on the RPV are prone to failure: the location of the focusing effect and location of in-core instrument penetration. These two potential points of damage in the RPV are investigated in this study. A numerical model for the prediction of the natural convection, melting, and solidification processes for IVR-ERVC is presented. The model is based on the enthalpy-porosity approach with an extension for continuous liquid fraction function. The model is implemented in open-source field operation and manipulation (OpenFOAM) computational fluid dynamic code to produce a new solver which is based on the combination of conjugate heat transfer solver and buoyant-driven natural convection solver and the new solver is validated against the melting Gallium experimental test, in-core instrumentation failure experimental test, and BALI experimental test. This numerical model is applied for the investigation of the RPV rupture at the location of the focusing effect and in-core instrumentation penetrations. Severe ablations of the cladding and the weld materials are observed at a heat load of about similar to 1800 K which is expected to lead to the ejection of the penetration tubes if the force holding the penetration tube in place is lower than the force exerted by the system pressure. Subsequently, a two-layer IVR configuration is assessed and the integrity of the RPV is found not to be compromised under external reactor vessel cooling. However, in the case of a boiling crisis, the temperature of the ex-vessel wall is expected to rise quickly and this is simulated by increasing the exvessel wall temperature. The RPV is found to fail near the beltline due to a phenomenon known as focusing effect when the ex-vessel wall temperature rises above 1200 K.