Recent Analytical and Computational Developments on the Advection-Diffusion-Reaction Wildfire Model

Abstract

Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematical modelling is essential for damage mitigation and risk assessment. This paper provides a comprehensive review of a physics-based Advection-Diffusion-Reaction (ADR) model, focusing on the balance between physical accuracy and computational efficiency. We analyze the ability of the ADR model to estimate fire front speed and behaviour and discuss its preliminary mathematical properties. Additionally, we discuss some modelling improvements which enhance the physical realism of the model. Furthermore, we address the challenge of reducing computational costs, emphasizing the need for inexpensive but precise numerical schemes. We report recent findings outlining open challenges in model discretization and technological solutions. All these developments highlight the potential of ADR models as powerful tools for efficient wildfire simulation and risk assessment.