This study investigates the mechanisms of macro-scale melting, in which the solid and liquid phases are separated by a defined interface. The main objective of our ongoing study is to develop a reliable numerical modeling which combines the general enthalpy formulation, convective heat transfer and rigid body sinking motion. Therefore, an advanced numerical model is developed and implemented using an in-house numerical code, built especially for this study. The numerical results were tested against benchmarks from the literature with gradually increasing complexity for which a good comparison was obtained. Then, the model is used to explore a case study of a cylindrical enclosure with isothermally heated bottom and side wall and insulated top wall. Two cases of temperature differences were investigated initially by assessing the melting patterns observed. The results were then generalized using dimensional analysis. The work illustrates that the new model can be applied to solve complex melting problems in axisymmetric geometry. The validated numerical model can now be used to investigate more cases, e.g. different aspect ratios and temperature conditions.