Abstract
Numerical simulation can be key to the understanding of the multi-dimensional nature of transient detonation waves. However, the accurate approximation of realistic detonations is demanding as a wide range of scales needs to be resolved. This paper describes a successful solution strategy that utilizes logically rectangular dynamically adaptive meshes. The hydrodynamic transport scheme and the treatment of the non-equilibrium reaction terms are sketched. A ghost fluid approach is integrated into the method to allow for embedded geometrically complex boundaries. Large-scale parallel simulations of unstable detonation structures of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures demonstrate the efficiency of the described techniques in practice. In particular, computations of regular cellular structures in two and three space dimensions and their development under transient conditions, i.e. under diffraction and for propagation through bends are presented. Some of the observed patterns are classified by shock polar analysis and a diagram of the transition boundaries between possible Mach reflection structures is constructed.