A new volume fraction formulation based fixed grid approach is developed for the numerical solu-tion of phase change problems. Instead of the traditional energy conservation equation where density wasconstant, a revised energy conservation equation is formulated where density varies with phase change. Avolume fraction updating scheme is proposed which is capable of evaluating the solid and liquid volumefractions during solidification and melting process. For the analysis, a two-dimensional rectangular cavitywith the riser is considered and cooling initiates from the bottom surface. Comparative analysis is carriedout for different aspect ratio of the cavity for the following case:- interaction between the shrinkage-inducedfluid flow and the natural convection due to temperature gradient. A comparison is also made by solvingthe system of governing equations using SIMPLE and SIMPLER algorithm. The results obtained via thesetwo algorithms are analyzed. A particular attention was given to the implementation of pressure boundarycondition at the top face of the riser which is connected to a source filled with molten metal.