Theoretical and numerical structure for unstable one-dimensional detonations
SIAM Journal on Applied Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension
Journal of Computational Physics
On the analysis and construction of perfectly matched layers for the linearized Euler equations
Journal of Computational Physics
Numerical Simulation of Pulse Detonation Engine Phenomena
Journal of Scientific Computing
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
Journal of Computational Physics
Numerical study on propagation of explosion wave in h2-o2 mixtures
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
Journal of Computational Physics
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In this paper, we demonstrate the detailed numerical studies of three classical two dimensional detonation waves by solving the two dimensional reactive Euler equations with species with the fifth order WENO-Z finite difference scheme (Borges et al. in J. Comput. Phys. 227:3101---3211, 2008) with various grid resolutions. To reduce the computational cost and to avoid wave reflection from the artificial computational boundary of a truncated physical domain, we derive an efficient and easily implemented one dimensional Perfectly Matched Layer (PML) absorbing boundary condition (ABC) for the two dimensional unsteady reactive Euler equation when one of the directions of domain is periodical and inflow/outflow in the other direction. The numerical comparison among characteristic, free stream, extrapolation and PML boundary conditions are conducted for the detonation wave simulations. The accuracy and efficiency of four mentioned boundary conditions are verified against the reference solutions which are obtained from using a large computational domain. Numerical schemes for solving the system of hyperbolic conversation laws with a single-mode sinusoidal perturbed ZND analytical solution as initial conditions are presented. Regular rectangular combustion cell, pockets of unburned gas and bubbles and spikes are generated and resolved in the simulations. It is shown that large amplitude of perturbation wave generates more fine scale structures within the detonation waves and the number of cell structures depends on the wave number of sinusoidal perturbation.