Numerical resolution of pulsating detonation waves

The canonical problem of the one-dimensional, pulsating, overdriven detonat ion wave has been studied for over 30 years, not only for its phenomenologi cal relation to the evolution of multidimensional detonation instabilities, but also to provide a robust, reactive, high-speed flowfield with which to test numerical schemes. The present study examines this flowfield using hi gh-order, essentially non-oscillatory schemes, systematically varying the l evel of resolution of the reaction zone, the size and retention of informat ion in the computational domain, the initial conditions, and the order of t he scheme. It is found that there can be profound differences in peak press ures as well as in the period of oscillation, not only for cases in which t he reaction front is under-resolved, but for cases in which the computation is corrupted due to a too-small computational domain. Methods for estimati ng the required size of the computational domain to reduce costs while avoi ding erroneous solutions are proposed and tested.