Analytical and numerical insights into wildfire dynamics: Exploring the advection-diffusion-reaction model

TL;DR

This paper investigates wildfire dynamics using an advection-diffusion-reaction model, analyzing the effects of wind and parameters through numerical simulations and linearization techniques to improve understanding and prediction of wildfire behavior.

Contribution

It provides a systematic analysis of a nonlinear wildfire model, highlighting the roles of different mechanisms and introducing linearization methods for better speed estimation.

Findings

Wind significantly influences wildfire propagation speed.

Model parameters like density and heating value affect biomass remaining.

Linearized models offer accurate estimates of propagation speed.

Abstract

Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents a systematic study of a widely used advection-diffusion-reaction wildfire model with non-linear coupling. The importance of single mechanisms is discovered by analysing hierarchical sub-models. Numerical simulations provide further insight into the dynamics. As a result, the influence of wind and model parameters such as the bulk density or the heating value on the wildfire propagation speed and the remaining biomass after the burn are assessed. Linearisation techniques for a reduced model provide surprisingly good estimates for the propagation speed in the full model.