A general model for wildfire propagation with wind and slope
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arXiv
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| Format: | Preprint |
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2021
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| author | Javaloyes, Miguel Ángel Pendás-Recondo, Enrique Sánchez, Miguel |
| author_facet | Javaloyes, Miguel Ángel Pendás-Recondo, Enrique Sánchez, Miguel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03364 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A general model for wildfire propagation with wind and slope Javaloyes, Miguel Ángel Pendás-Recondo, Enrique Sánchez, Miguel Differential Geometry Mathematical Physics 53C80, 53C22, 53C60 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. |
| title | A general model for wildfire propagation with wind and slope |
| topic | Differential Geometry Mathematical Physics 53C80, 53C22, 53C60 |
| url | https://arxiv.org/abs/2110.03364 |