In the event of a severe accident in a nuclear reactor involving reactor core degradation, molten core materials called Corium can form. The interaction of Corium with the concrete of reactor containment buildings may threaten the integrity of nuclear power plants. A technical solution to prevent the penetration of Corium into the concrete base-mat is the implementation of a core-catcher designed to collect the Corium and spread it over a large area to be cooled efficiently. Due to the complexity of Corium spreading simulations, standard numerical methods used in Computational Fluid Dynamics (CFD) may not be applicable to Corium flows. Therefore, the work presented in this thesis investigates in detail the errors associated with the numerical simulation of Corium flows. In particular, the numerical representation of the interface between two immiscible fluids, such as Corium and air, is challenging. This thesis identifies numerical diffusion of temperature, which is a numerical error associated with the spatial discretisation process, in the vicinity of the Corium/air interface, as a source of error for Corium spreading simulations. A numerical strategy is proposed and evaluated on several test cases with known solutions. It is shown that, compared to standard numerical methods, the proposed strategy significantly reduces numerical diffusion. The numerical methods studied in this thesis are validated against experimental results from the VULCANO VE-U7 Corium spreading experiment. The simulation results obtained are compared to experimental results as well as other simulation results available in the scientific literature. It is shown that the choice of numerical methods affects the spreading predictions, however, the uncertainty of Corium properties is the major source of uncertainty in the simulation results