Some numerical issues on simulation of detonation cell structures

The present study examines several numerical issues on simulation of detonation cell structures. Various stability regimes ranging from weakly to highly unstable detonations are considered. The analysis treats two-dimensional inviscid fluid-dynamics equations and a one-step reaction model. A series of investigations is carried out to identify numerical requirements for high-fidelity simulations of detonation cell structures. Emphasis is placed on the wave-front dynamics and evolution of cellular patterns. The effects of the preexponential factor, grid size, time step, domain length, and exit boundary condition on the cellular structure and cell size are examined systematically. The required numerical grid size is determined and compared with various length scales associated with a steady Zel’dovich–von Neumann–Döring detonation wave. A general rule for the grid-resolution requirement is proposed for the first time: a minimum of 5 grid points should be included in the heat-release zone of the corresponding steady Zel’dovich–von Neumann–Döring detonation wave, in order to achieve an accurate simulation of detonation cell structures.