An enthalpy-porosity fixed-grid method has been applied to the melting and solidification of pure metals in a rectangular cavity. Flow structures and isotherms are compared with literature information based on multidomain analysis. During solidification, recirculation cells are observed to vanish with time, whereas the multidomain method predicted their enlargement. The cell near the interface significantly affects the local solidification rate at the cavity top. Results of the present study agree well with the experimental data in the literature. The effect of neglecting the viscous diffusion term for a phase change problem involving low Prandtl number liquid metals is also studied. The maximum value of the stream function is higher by 10% and the melt volume by 5%, in the absence of viscous effects.