Simulation plays a crucial role on the management of subsurface oil reservoirs. Its ability to predictthe complex behaviour of fluid flow in highly heterogeneous porous media allows us to optimize productions levels in accordance with the economic needs. Optimization and history matching techniques make an extensive use of this tool to better understand, and to forecast the different scenarios and their impact on the production curves. However, the recent advancements in characterization have allowed the petro-physical data to be integrated in scale with orders of magnitude higher than the scale of standard petroleum reservoir simulators. To deal with this discrepancy, the  Multiscale Finite Volume (MsFV) family of approximate and conservative methods have been develop. These schemes project the fine-scale system of equation onto a coarse-space, where it is solved and projected back. This way, the high-resolution data is integrated to the simulator model allowing fast and robust solutions at the price of a small loss of accuracy.  Nonetheless, the MsFV family is unfit to handle simulations  on non k-orthogonal grids. This work aims to study techniques to generalize methods in the Finite Volume and Multiscale Finite Volume families in order to expand their applications to general unstructured grids.