Commercial programs are widely used to do unstructured and structured meshes for CFD simulations. However, grids and meshes based on free-open source software (FOSS) give to researchers and engineers the possibility to adapt and improve the meshing process for special study cases with a high Reynolds numbers, such as unsteady partial cavitating flows. In order to improve the grid qualities, the FOSS GMSH has been used to do three types of grid, unstructured hexahedral mesh, hybrid mesh and structured hexahedral mesh for the simulation of partial cavitation around a plane-convex hydrofoil. Numerical simulations have been carried out by using the FOSS OpenFOAM based on the Zwart cavitation model and the implicit large eddy simulation (ILES). The results show that the structured mesh provides the best simulating to experimental data. On the other hand, the hybrid mesh induces unreliable results at leading edge without shedding.