Abstract: The invention relates to a method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein. The method includes determining a time-step for simulating the reservoir, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations, calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions of the reservoir model corresponding to the time-step, the plurality of CFL conditions comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, simulating a first cell of the plurality of gridded cells with an Implicit Pressure, Explicit Saturations (IMPES) system, and simulating a second cell of the plurality of gridded cells with a Fully Implicit Method (FIM) system.