2024/10/02 by Nieding, Luca, Reisch, Cordula, Langemann, Dirk +1
#35K57 #65M12 #92F05 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2410.02837
Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely used to study wildfire dynamics. In this study, we introduce the previously unconsidered influence of topography through an additional advective term. Furthermore, we propose a linear term for the combustion function, comparing it with the commonly used Arrhenius law to offer a simpler model for further analysis. Our findings on the model's dynamics are supported by numerical simulations showing the differences of model extensions and approximations.