A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
by C. Helzel, R. J. LeVeque, and G. Warnecke, SIAM J. Sci. Comput., 22 (2000) 1489-1510.

Abstract. The numerical approximation of combustion processes may lead to numerical difficulties, which are caused by different time scales of the transport part and the reactive part of the model equations. Here we consider a modified fractional step method that overcomes this difficulty on standard test problems and allows the use of a mesh width and time step determined by the nonreactive part, without precisely resolving the very small reaction zone. High-resolution Godunov methods are employed and the structure of the Riemann solution is used to determine where burning should occur in each time step. The modification is implemented in the software package CLAWPACK. Numerical results for 1D and 2D detonation waves are shown, including a detonation wave diffracting around a corner.

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bibtex entry:

@Article{ch-rjl-gw:deton,
  author =       "C. Helzel and R. J. LeVeque and G. Warnecke",
  title =        "A Modified Fractional Step Method for the Accurate
                 Approximation of Detonation Waves",
  journal =      "SIAM J. Sci. Comput.",
  year =         "2000",
  volume =       "22",
  pages =        "1489--1510",
  doi =          "10.1137/S1064827599357814"
}