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

TL;DR

This paper enhances wildfire modeling by incorporating topography effects and proposing a simplified combustion function, with numerical simulations demonstrating the impact of these extensions on fire front propagation.

Contribution

It introduces the influence of topography via an advective term and proposes a linear combustion function as a simpler alternative to the Arrhenius law.

Findings

Topography significantly affects fire front dynamics.

Linear combustion model provides comparable results to Arrhenius law.

Numerical simulations highlight differences in model extensions.

Abstract

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.