Application of Front Tracking to Two-Dimensional Curved Detonation Fronts

Abstract

This is the first of a series of papers describing a program which has a potential for achieving a significant improvement in the numerical modeling of detonation waves. In this paper, we establish the convergence of the front tracking method for two-dimensional detonation problems. The Chapman–Jouguet (CJ) thin flame model is used. An iterative method for the solution to these model equations, and for which we prove convergence, is described. We then take as a test problem a cylindrically symmetric expanding strong detonation wave. The solution to the model equations in this geometry by the random choice method with operator splitting computed on a fine grid is taken to be exact. The convergence of the front tracking solution to this solution is discussed and convergence rates are established. The methods described above use planar detonation wave speeds. Corrections due to curvature are needed especially for unsupported diverging detonations. This issue will be addressed in the next paper in this series.