A general model for wildfire propagation with wind and slope

A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies and slope of the ground) is introduced. It relies on a general theoretical framework, which reduces the hyperbolic PDE system of any wave t...

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Bibliographic Details
Published inarXiv.org
Main Authors Javaloyes, Miguel Ángel, Pendás-Recondo, Enrique, Sánchez, Miguel
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.08.2024
Subjects
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Time dependence
Time measurement
Wave fronts
Wildfires
Wind effects
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Summary:A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies and slope of the ground) is introduced. It relies on a general theoretical framework, which reduces the hyperbolic PDE system of any wave to an ODE in a Lorentz-Finsler framework. The wind induces a sort of double semi-elliptical fire growth, while the influence of the slope is modeled by means of a term which comes from the Matsumoto metric (i.e., the standard non-reversible Finsler metric that measures the time when going up and down a hill). These contributions make a significant difference from previous models because, now, the infinitesimal wavefronts are not restricted to be elliptical. Even though this is a technical complication, the wavefronts remain computable in real time. Some simulations of evolution are shown, paying special attention to possible crossovers of the fire.
ISSN:2331-8422
DOI:10.48550/arxiv.2110.03364