{"title":"A Simple but Effective Bushfire Model: Analysis and Real-Time Simulations","authors":"Serena Dipierro, Enrico Valdinoci, Glen Wheeler, Valentina-Mira Wheeler","doi":"10.1137/24m1644596","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1504-1514, August 2024. <br/> Abstract. 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 environmental wind and of the pyrogenic flow. The simplicity of the model is highlighted by the fact that it is described by a single scalar equation, containing only four terms, making it very handy for rapid and effective numerical simulations which run in real time. In spite of its simplicity, the model is in agreement with data collected from bushfire experiments in the lab, as well as with spreading of bushfires that have been observed in the real world. Moreover, the equation describing the temperature evolution can be easily linked to a geometric evolution problem describing the level sets of the ignition state.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m1644596","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1504-1514, August 2024. Abstract. 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 environmental wind and of the pyrogenic flow. The simplicity of the model is highlighted by the fact that it is described by a single scalar equation, containing only four terms, making it very handy for rapid and effective numerical simulations which run in real time. In spite of its simplicity, the model is in agreement with data collected from bushfire experiments in the lab, as well as with spreading of bushfires that have been observed in the real world. Moreover, the equation describing the temperature evolution can be easily linked to a geometric evolution problem describing the level sets of the ignition state.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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