This study investigates numerically a silicon-based latent heat storage system operating at ultra-high temperatures (similar to 1410-2000 degrees C). Owing to the silicon's high latent heat (1230 kWh.m(-3)), storage densities of almost an order of magnitude higher than the state-of-the-art molten salt-based systems can be achieved. Prior to fabricating this system, there is a necessity to scrutinize the complex heat transfer mechanisms occurring during silicon phase change and indicate a vessel design that enables quick charge rates. A validated transient computational fluid dynamics model, combining the multiphase volume of fluid method with the enthalpy porosity approach and an adaptive local grid refinement technique is applied. This model simultaneously takes into account the phase-change material (PCM) volumetric change and the effect of dendritic formations and buoyancy -driven natural convection on the melting process. Numerical results reveal that the system charge rate is highly dependent on the PCM permeability, vessel design and operating conditions. Between five shapes investigated, i.e. cube, truncated cone, sphere, cut-off sphere and cylinder of volume V = 3.75E-03 m(3), the truncated cone is the most preferable considering both design flexibility- its height can be easily altered, without increasing its volume- and melting rates. Actually, the PCM melting time achieved with the cone is 21% quicker compared to sphere and 6% slower compared to cube. Concerning the vessel size, the melting time increases by almost 28%, when the vessel volume increases to V' = 2V. Finally, reduction in the silicon melting time, almost by 31%, is achieved by increasing the Stefan number by 35%.