In the present study, direct numerical simulations for smouldering in a horizontal channel are performed for both compressible and incompressible flows. The reactant gas is passing through the char surface, where the chemical reaction is going to take place. For the sake of simplicity, the smouldering is treated to be a single step chemical reaction. In the incompressible flow, a set of governing parameters are discussed to elucidate their influences on the process of smouldering. Furthermore, the variations of density and dynamic viscosity of gaseous mixture are taken into account in the compressible flow. The comparison between the compressible and incompressible flows reveals that the effects of local compressibility and gaseous mixture on the propagation of smouldering wave are trivial.