Impact of topography and combustion functions on fire front propagation in an advection-diffusion-reaction model for wildfires

The paper correctly identifies and mitigates spurious heating from a divergent topographic advection term and shows (numerically) that a linearized combustion law reproduces Arrhenius-like traveling fronts. However, it offers no rigorous analytical proof and defines the topflow correction via an area-averaged flux that does not imply pointwise cancellation of divergence. The model’s solution gives a clear local derivation of spurious heating and a stronger correction (w̃ = −∇·v) that would eliminate it pointwise, but this differs from the paper’s definition. Its traveling-wave derivation relies on thin-zone and completeness assumptions (Y(−∞)=0) that are not stated in the paper and contains a sign mix-up in the outer eigenvalues; the front-speed formula is not established in the paper. Hence both are incomplete: the paper is primarily phenomenological, and the model’s proof attempt needs corrected hypotheses and sign conventions.