Numerical modeling of heat transfer during solidification has become widespread in the foundry industry. This is because it is possible to investigate the effects of adjustment to the casting variables on final casting quality, without having to do costly trial-and-error experiments. After selecting a suitable mathematical model, one has to choose an appropriate discretization method. If the grid is very fine, each type of method yields the same solution. However, some methods are more suitable to some classes of problems than others. The main objective of this paper is to demonstrate the advantages of using a block unstructured grid in combination with a generalized curvilinear formulation in a casting scenario and compare the performance of two discretization methods, finite differences (FD) and finite volume (FV). The validation of the numerical procedure is done by comparison with measurements which experimental set up is also described. A very good agreement of both numerical methods were verified with a slightly advantage for the finite volume method. Block unstructured grids works well with both discretization methods, allows obtain any physical feature in specific positions of the domain and is suitable for parallel computation; in combination with a generalized curvilinear formulation allows avoid geometric complexities and the development of more efficient algorithms..