A Simple but Effective Bushfire Model: Analysis and Real-Time Simulations

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-15 DOI:10.1137/24m1644596

Serena Dipierro, Enrico Valdinoci, Glen Wheeler, Valentina-Mira Wheeler

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.

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简单而有效的丛林火灾模型：分析和实时模拟

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1504-1514 页，2024 年 8 月。摘要。我们为丛林火灾引入了一个简单的数学模型，该模型考虑了在给定点火状态以上激活的燃烧项存在时的温度扩散。该模型还考虑了环境风和火源流的影响。该模型的简单性突出表现在它是由单个标量方程描述的，只包含四个项，这使得它非常便于进行快速有效的实时数值模拟。尽管该模型非常简单，但它与实验室丛林火灾实验收集的数据以及在现实世界中观察到的丛林火灾蔓延情况相吻合。此外，描述温度演变的方程很容易与描述点火状态水平集的几何演变问题联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

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.