Kinetic formulation of linear stability for steady detonation waves (Q2726126)

The aim is to re-address the stability formulation of a detonation wave within a discrete kinetic framework, and to show the capability of kinetic models to study the linear stability, according to the classical treatment. A class of discrete kinetic models for detonating gases with a quite general reversible chemical reaction is characterized, and the response of the steady detonation solution to small rear boundary perturbations is investigated at a microscopic scale. The contents of the paper is arranged in six sections. In section 2, the authors summarize the relevant mathematical aspects of a discrete model which can be adopted to describe the reactive flow. In section 3 the procedure necessary to recover detonation wave solutions is briefly outlined. Section 4 presents the stability problem. In particular, the governing equations and related Rankine-Hugoniot conditions are transformed to the wave coordinate, and then are linearized about the steady solution through a normal expansion. In section 5, an acoustic analysis is performed at the end of the reaction zone, and a radiation condition is imposed in order to derive the dispersion relation for normal modes. Finally, in section 6, the authors formulate the stability problem for a general class of kinetic models, and establish a criterion for linear detonation stability.