We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate v(f) in a shear flow increases with compressibility intensity ε, following the relation Δv(f)~ε(2). Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case. The effect has been quantitatively measured, and it turns out to be generally small. For the cellular flow, two extreme cases have been investigated, with the whole perturbation situated either in the center of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behavior in the two cases. The enhancing remains modest and is always less than 20%.

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