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Article

Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires

1
CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
2
Departamento de Silvicultura, Facultad de Ciencias Forestales, Universidad de Concepción, Casilla 160-C, Concepción 4070374, Chile
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Departament de Matemàtiques, Universitat de València, Av. Vicent Andrés Estellés, E-46100 Burjassot, Spain
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GIMNAP-Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción 4051381, Chile
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CI2MA, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1034; https://doi.org/10.3390/math8061034
Received: 13 April 2020 / Revised: 21 June 2020 / Accepted: 23 June 2020 / Published: 24 June 2020
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment)
Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-linear parabolic term and the stiffness in the reactive part. Weighted essentially non-oscillatory (WENO) reconstructions are applied to the discretization of the nonlinear convection term. Examples are focused on the applicative problem of determining the width of a firebreak to prevent the propagation of forest fires. Results illustrate that the model and numerical scheme provide an effective tool for defining that width and the parameters for control strategies of wildland fires. View Full-Text
Keywords: forest fire model; numerical solution; firebreak; convection-diffusion-reaction problem; implicit-explicit time integration; weighted essentially non-oscillatory reconstruction forest fire model; numerical solution; firebreak; convection-diffusion-reaction problem; implicit-explicit time integration; weighted essentially non-oscillatory reconstruction
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MDPI and ACS Style

Bürger, R.; Gavilán, E.; Inzunza, D.; Mulet, P.; Villada, L.M. Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires. Mathematics 2020, 8, 1034. https://doi.org/10.3390/math8061034

AMA Style

Bürger R, Gavilán E, Inzunza D, Mulet P, Villada LM. Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires. Mathematics. 2020; 8(6):1034. https://doi.org/10.3390/math8061034

Chicago/Turabian Style

Bürger, Raimund; Gavilán, Elvis; Inzunza, Daniel; Mulet, Pep; Villada, Luis M. 2020. "Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires" Mathematics 8, no. 6: 1034. https://doi.org/10.3390/math8061034

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