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

Raimund Bürger, Elvis Gavilán, Daniel Inzunza, Pep Mulet and Luis Miguel Villada
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Raimund Bürger: CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
Elvis Gavilán: Departamento de Silvicultura, Facultad de Ciencias Forestales, Universidad de Concepción, Casilla 160-C, Concepción 4070374, Chile
Daniel Inzunza: CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
Pep Mulet: Departament de Matemàtiques, Universitat de València, Av. Vicent Andrés Estellés, E-46100 Burjassot, Spain
Luis Miguel Villada: GIMNAP-Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción 4051381, Chile

Mathematics, 2020, vol. 8, issue 6, 1-21

Abstract: 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.

Keywords: forest fire model; numerical solution; firebreak; convection-diffusion-reaction problem; implicit-explicit time integration; weighted essentially non-oscillatory reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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