Shock-Fitted Numerical Solutions of One- and Two-Dimensional Detonation

One- and two- dimensional detonation problems are solved using a conservative shock-fitting numerical method which is formally fifth order accurate. The shock-fitting technique for a general conservation law is rigorously developed, and a fully transformed time-dependent shock-fitted conservation form is found. A new fifth order weighted essential non-oscillatory scheme is developed. The conservative nature of this scheme robustly captures unanticipated shocks away from the lead detonation wave. The one-dimensional Zel'dovich-von Neumann-Doering pulsating detonation problem is solved at a high order of accuracy, and the results compare favorably with those of linear stability theory. The bifurcation behavior of the system as a function of activation energy is revealed and seen to be reminiscent of that of the logistic map. Two-dimensional detonation solutions are found and agree well with results from linear stability theory. Solutions consisting of a two-dimensional detonation wave propagating in a high explosive material which experiences confinement on two sides are given which converge at high order.