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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...
The positivity-preserving well-balanced discontinuous Galerkin (DG) method (Xing et al. J Sci Comput 57, 2013) is employed to solve the shallow water equations on an unstructured triangular mesh and to study their applications in computational hydrology. The grid convergence of the DG method is verified via the steady state oblique hydraulic jump problem. The dam-breaking problems with wet and dry...
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