One-dimensional dynamics of gaseous detonations revisited

Stability of one-dimensional gaseous detonations is revisited using both asymptotic analysis and high-order numerical simulations. The double limit small heat release a ratio specific heats close to unity considered, attention focused on weakly unstable in the Chapman-Jouguet regime. It shown that time-dependent velocity lead shock can be obtained as eigenfunction hyperbolic problem reducing single equation for flow. solution then expressed form an integral velocity, from which threshold activation energy transition instability oscillation frequency obtained. These theoretical findings are validated against set direct simulations same limit, performed spectral difference scheme particular care taken ensure high resolution flow with minimal dissipation, while also suppressing post-shock aberrations. Values detonation parameters at systematically compared their counterparts, confirming validity proposed theory.