A physics-based simplified model for simulating wildfire spread in heterogeneous environments

Due to climate change, there is an urgent call for scientific research into the prevention and mitigation of wildfires. Within the last 50 years, mathematical models for forest fire propagation have been developed to understand and predict the evolution of fire. In this work, we present a simplified Advection-Diffusion-Reaction (ADR) model that is physics-based and accounts for the effects of environmental conditions, topography, and the distribution and heterogeneity of fuel. The model consists of two equations: a partial differential equation for the conservation of energy and an ordinary differential equation for the evolution of biomass. It explicitly represents fuel moisture effects by means of the apparent calorific capacity method, distinguishing between live and dead fuel moisture content. Although simplified, the model is derived from the theory of two-phase porous flows and emphasizes a robust theoretical foundation. Using this model, we conduct exploratory simulations and present theoretical insights into various modeling decisions in the context of ADR-based models. We seek to understand the interplay between the different mechanisms involved in wildfire propagation, to identify key factors influencing fire spread, and to estimate the model's predictive capacity. We show that the model results are consistent with laboratory experiments and field observations by carrying out parametric analyses and qualitative comparisons. The rate of spread predicted by the model exhibits an exponentially decaying trend with increasing fuel moisture and a Ricker function-like behavior with changes in bulk density, which is consistent with previous literature. The results herein presented help build confidence in the model’s predictive capability and motivate further steps towards the application of the model to real-world scenarios.