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

Author

Listed:
  • 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
    CI2MA, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile)

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.

Suggested Citation

  • Raimund Bürger & Elvis Gavilán & Daniel Inzunza & Pep Mulet & Luis Miguel Villada, 2020. "Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1034-:d:375683
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    Cited by:

    1. Raimund Bürger & Elvis Gavilán & Daniel Inzunza & Pep Mulet & Luis Miguel Villada, 2020. "Exploring a Convection–Diffusion–Reaction Model of the Propagation of Forest Fires: Computation of Risk Maps for Heterogeneous Environments," Mathematics, MDPI, vol. 8(10), pages 1-20, October.

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