Stability and interval selection in the numerical integration of the equations describing ignition in a turbulent flow

An analysis is carried out of the stability of a linearized system of telegraphic equations, proposed as a model for studying the ignition of gas mixtures containing toxic components (methyl mercaptan etc.). The ignition is assumed to be related to the set of aerodynamic and kinetic parameters at which the system begins to be unstable. An analysis of the spectrum of growing disturbances indicates that their short-period part cannot be described sufficiently accurately using the difference methods of second-order accuracy usually applied in numerical studies. Instead a difference method correct to terms of fourth order must be used. The proposed method provides an efficient determination of the intervals of the time and space coordinates as functions of the main turbulent and kinetic parameters for the solution of ignition problems.