Qualitative modeling of the dynamics of detonations with losses

We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qualitative level, the essential properties of unsteady detonation waves, including pulsating and chaotic solutions. In particular, we investigate the effects of shock curvature and friction losses on detonation dynamics. To calculate steady-state solutions, a novel approach to solving the detonation eigenvalue problem is introduced that avoids the well-known numerical difficulties associated with the presence of a sonic point. By using unsteady numerical simulations of the simplified model, we also explore the nonlinear stability of steady-state or quasi-steady solutions.