Comparing Shock-Attached and Lab Frames of Reference for Numerical Simulations of Two-Dimensional Channel Detonations

Numerical simulation of two-dimensional detonations in channels using detailed chemistry presents a formidable computational challenge with stiff requirements on resolution and timestepping. The computational load is exacerbated further due to the long channel lengths required to ensure that the observed dynamics are not merely a remnant of the initial condition. Despite the progress in Adaptive Mesh Refinement (AMR), we note that the base grid in such simulations still becomes quite large for long channels. Consequently, computations in the shock-attached frame offer an attractive alternative to enable unprecedentedly long simulation times thereby effectively enabling simulations of detonation waves through very long channels at a reduced cost due to the smaller domain needed. While the shift to the shock frame looks to be straightforward for ZND calculations due to the constant wave speed, the question of their equivalence for multi-dimensional detonations (particularly for highly irregular detonations of mixtures with high activation energies) remains unanswered, due to the fluctuating detonation wave speed arising from cellular structures. In this work, we rigorously analyze and demonstrate the equivalence of the two frames of reference for two dimensional detonations for both a regular H₂/air mixture and an irregular C₂H₂/O₂/N₂ mixture with no-slip wall boundary conditions to account for viscous effects.