High order weighted essentially non-oscillation schemes for two-dimensional detonation wave simulations

Zhen Gao, Wai Sun DON*, Zhiqiu Li

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)80-101
Number of pages22
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - Oct 2012

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Detonation
  • Perfectly matched layer
  • Weighted essentially non-oscillatory
  • ZND


Dive into the research topics of 'High order weighted essentially non-oscillation schemes for two-dimensional detonation wave simulations'. Together they form a unique fingerprint.

Cite this