A numerical study is made of the melting of ice in a rectangular cavity filled with a porous medium subjected to multiple constant temperature heat sources. Focus is placed on establishing a computationally efficient approach for solving moving boundary heat transfer problem in a two-dimensional structured grids. Specific application to multidimensional melting problem with a complicated moving boundary condition is considered. Preliminary grids are first generated by an algebraic method, based on a transfinite interpolation method, with subsequent refinement using a PDE mapping (parabolic grid generation) method. A preliminary case study indicates successful implementation of the numerical procedure. A two-dimensional melting model is then validated against available analytical solution and experimental results and subsequently used as a tool for efficient computational prototyping.