Two approaches to the mathematical modeling of detonation waves

The work is dedicated to the numerical investigation of different propagation regimes of a gaseous pulsating detonation wave using two approaches. In the first one, the problem is solved in the laboratory frame and the detonation is initiated near the closed end of the channel. In the second approach, the simulation is carried out in the shock-attached frame. For this purpose, a second approximation order algorithm for the integration of the shock evolution equation using the grid-characteristic method is proposed. The stable, weakly unstable, and irregular regimes of detonation wave propagation are investigated using both approaches. The qualitative and quantitative differences between the two approaches are put forward.