Related papers: Modelling wildfire spread and spotfire merger usin…
The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a novel geometric structure where the…
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…
Atmospheric pollution regulations have emerged as a dominant obstacle to prescribed burns. Thus, forecasting the pollution caused by wildland fires has acquired high importance. WRF and SFIRE model wildland fire spread in a two-way…
The increasing incidence and severity of wildfires underscores the necessity of accurately predicting their behavior. While high-fidelity models derived from first principles offer physical accuracy, they are too computationally expensive…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
Level set methods are versatile and extensible techniques for general front tracking problems, including the practically important problem of predicting the advance of a firefront across expanses of surface vegetation. Given a rule,…
Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based…
Wildfires are among the most severe disturbances affecting forest ecosystems, with over 50,000 hectares burned in Patagonia, Argentina, during 2025 alone. This study implements a Reaction-Diffusion-Convection (RDC) model to simulate…
We introduce a simple mathematical model for bushfires accounting for temperature diffusion in the presence of a combustion term which is activated above a given ignition state. The model also takes into consideration the effect of the…
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition…
Understanding how intrinsically fast hydrogen-air premixed flames can be rendered much faster in turbulence is crucial for systematically developing hydrogen-based gas turbines and spark ignition engines. Here, we present fundamental…
Modelling wildfire occurrences is important for disaster management including prevention, detection and suppression of large catastrophic events. We present a spatial Poisson hurdle model for exploring geographical variation of monthly…
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…
This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite…
Predicting future states in uncertain environments, such as wildfire spread, medical diagnosis, or autonomous driving, requires models that can consider multiple plausible outcomes. While diffusion models can effectively learn such…
Fire propagation is a major concern in the world in general and in Argentinian northwestern Patagonia in particular where every year hundreds of hectares are affected by both natural and anthropogenic forest fires. We developed an efficient…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…
This study presents methane-air counterflow simulations, in computationally efficient similar form, allowing combustible mixtures to flow from one or both directions in order to learn more about multi-branched propagating flame structures…
For the time-parallel Parareal method, there exists both numerical and analytical proof that it converges very well for diffusive problems like the heat equation. Many applications, however, do not lead to simple homogeneous diffusive…