Global asymptotic effects of the structure of combustion waves in porous media

In this work we study gas solid combustion, with rate described by the laws of mass action, which states that the reaction rates are proportional to the available concentration of reactants, and of Arrhenius law. We consider a thermally insulated cylinder of porous rock containing solid fuel and a one dimensional flow along its axis. The thermal capacity of the gas is small. Reactive flow of air in the porous rock with solid fuel is governed by a system of balance equations for gas mass, oxygen mass, enthalpy and fuel mass. We are interested in examining the physical model supporting a combustion traveling wave, fuel and oxygen controlled, governed by parabolic partial differential equations. To solve numerically the Riemann problem, we use an implicit hybrid finite difference scheme with adaptive time step. The scheme is a combination of the classical Crank-Nicolson scheme and the Box scheme. We show that this hybrid scheme reproduces very well analytical solutions that can be obtained for certain simple flow conditions.