Slow-time acceleration for modeling multiple-time-scale problems

The numerical simulation of a system exhibiting a broad range of time scales can be very expensive because the time discretization will in general need to resolve the smallest time scale, and the simulation will have to extend over many times the longest time scale. However, it is common that not all the time scales are of interest for a particular problem. When the long time scales are of primary interest, a number of techniques are available to eliminate the unwanted short time scales from consideration. When the short time scales are of primary interest, a technique for mitigating the consequences of anomalously long time scales is needed. The “slow-time acceleration” technique presented here has been developed to address this problem. In the slow-time acceleration technique, a modified evolution equation is developed in which the longest time scale is much shorter than that of the original system, and which has the same multi-time scale asymptotic structure as the original system. As an example, this approach is applied to the numerical simulation of solid-propellant rockets in which the long time scale is associated with the regression of the burning propellant.