Dynamics and stability of one-dimensional combustion problems

The governing system including equations of gas mixture motion and an equation of a chemical kinetics is considered. The system describes combustion of gas mixture. The purpose of given work is a definition of parameters values, if the modes of stable combustion is possible, and definition of combustion front width and speed values for such mode. Under the construction of algorithms the principle of separating up processes was used: gas dynamics and convection on the one hand and diffusion and heat conduction on the other hand. For gas dynamics the explicit TVD scheme of order $O(\tau+h^2)$ and for thermodiffusive processes implicit scheme also of order $O(\tau+h^2)$ were constructed. As a result of calculations the thermodiffusive instabilities are established under evident difference of coefficients of thermal conduction and diffusion and availability of a stable mode under condition of $\mathrm{Le}\propto 1$, where $\mathrm{Le}$ is Lewis number, that is the first computational endorsement of known outcomes of Ya. B. Zeldovich and G. I. Barenblatt.