Simulation of a planar combustion wave

In this paper a planar combustion wave propagating in a gaseous mixture is simulated. The two-dimensional compressible Navier–Stokes equations for a reacting mixture of two species, burnt and unburnt gas, are considered. The unburnt gas is assumed to be converted into burnt gas by a one-step irreversible chemical reaction. The rate of production of the burnt gas is modelled according to the Arrhenius law. The resulting differential system is numerically integrated by means of a semi-implicit version of the alternating direction method. The scheme is so devised that its stability does not depend upon the speed of sound. If the computational grid is divided into n × m finite-difference cells, at each time step the algorithm requires the solution of n tridiagonal systems of m equations in m unknowns in the first stage, and of m tridiagonal systems of n equations in n unknowns in a second stage. All these systems are diagonally dominant with positive elements on the main diagonal and negative ones elsewhere. Thus existence and uniqueness of the numerical solution are assured. Finally, some computer examples are described and discussed.