Numerical simulations of traveling waves in a counterflow filtration combustion model

We focused on traveling combustion waves that appear in a simplified, one-dimensional combustion model in porous media. The system we consider is a reaction-convection-diffusion system that can be reduced into two-dimension in order to prove traveling waves by phase plane analysis. In previous studies combustion wave velocity was assumed positive and their existence was proven. Also, all possible wave sequences that solve boundary value problems on infinite intervals with constant boundary data were identified. In this study, we generalize the previous work by including the case of negative combustion wave speed and taking the assumption that oxygen is carried faster than temperature. Moreover, we extend the classification of all possible wave sequences by performing numerical simulations using finite difference scheme.

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