The 'method of characteristics' was proposed as a fast method of reservoir simulation many years ago. When gravitational effects are absent, the method results in a reservoir simulation technique identical to that of currently popular streamline models. However, the characteristic method rigorously includes gravity, whereas the streamline method does not. The characteristic method has never become popular, probably because of the lack of a criterion for locating the flood fronts in multiple dimensions. This problem is widely discussed in the mathematical literature, and seems to have become a classical paradox. This paper describes the use of a local material balance at points throughout the reservoir to establish the location of the front. The availability of this criterion makes the characteristic simulation method practical. The front location technique is fast, taking approximately the same amount of time as locating the constant saturation lines or characteristics. Hence, the method offers the speed of streamline simulators combined with the greater accuracy and versatility resulting from a rigorous treatment of gravitational effects. Examples of simulations from the new characteristic simulator are provided.