Three-dimensional detonation simulations with the mapped WENO-Z finite difference scheme

We perform a very long time numerical simulation to capture the three-dimensional detonation structures in a rectangular duct by solving the reactive Euler equations using the high order/resolution WENO-Z conservative finite difference scheme (Gao et al. J. Sci. Comput. 55: 351-371, 2013). In the algorithm, the perfectly matched layer (PML) absorbing boundary condition (ABC) for the reactive Euler equations is used to reduce the spurious wave reflection from the open left boundary which allows one to use a significant smaller truncated physical domain. Moreover, a tangent grid mapping is used to enhance the grid resolution within the half reaction zone that greatly reduces the memory usage and computational time compared with solving the problem with a uniform grid. The initial Zeldovich-von Neumann-Döring (ZND) profile of two classical stable and slightly unstable detonation waves is perturbed to generate the rectangular in-phase, diagonal in-phase and spinning detonation structures. Depending on the initial perturbation, the stable case shows the presence of a rectangular mode and a diagonal mode of the detonation front, which are suggested to be geometrically similar. The slightly unstable case, as expected, generates the spinning detonations instead in a narrow duct. The results show that a short time simulation is insufficient to capture the cellular detonation structures. The width-to-length ratio of the cellular patterns depends on the gas properties only, but independent of the perturbation of the initial conditions.