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