Modeling of linear stability of planar detonation waves in extended kinetic theory

The classical linear stability of the steady detonation wave with finite reaction zone is here studied within kinetic theory extended to chemically reacting gases with a two-way bimolecular reaction. The Euler equations and the Rankine-Hugoniot conditions of the kinetic model are linearized through a normal mode expansion around the steady detonation solution which is known from a previous paper. The linear stability is formulated by means of a non closed system of unknown perturbations with initial data at von Neumann state. A dispersion relation at the end of the reaction zone assures its determinacy.