Recent advances in applications of geostatistics to reservoir characterization have produced increasingly sophisticated geological models which have put considerable demands on the engineer's ability to do rapid reservoir performance evaluation. With this motivation in mind, a new method for fast reservoir simulation based on an unconventional formulation has been developed. This formulation has flux-based unknowns, in contrast to more conventional approaches which typically have pressure-based unknowns. For a useful range of conditions, the flux-based unknowns experience little or no variation over time throughout most of the reservoir domain, enabling fast simulations of fluid movement in the reservoir. In conjunction with iterative solvers that dynamically adapt to conditions in the reservoir, this formulation has been used to create a new simulator, designated as FMF (for Flux-based Multi-phase Flow). The FMF algorithm includes a rigorous mass conservation scheme that maintains accurate material balance throughout the entire simulation. Studies of overall accuracy and computational efficiency for a series of case studies have been carried out with the simulator. These studies are based on comparisons with Eclipse, with all computations done on a common platform to facilitate CPU timing studies. For the cases considered, these studies have revealed that the FMF algorithm is approximately one order of magnitude faster than Eclipse, and produces similar results.