Ngen-Kütral: Toward an Open Source Framework for Chilean Wildfire Spreading

Martin, Daniel; Torres, Claudio E.

doi:10.1109/sccc.2018.8705159

Cited by 7 publications

(13 citation statements)

References 18 publications

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“…where the vector field w 0 (x, t) is a given wind velocity that may depend on spatial position and time (but is considered constant in our numerical experiments), and T (x) is the topography of the domain [10,11]. This choice differs from that of [1], where the terrain was assumed flat, and allows us to include spatial heterogeneity.…”

Section: Summary Of the Mathematical Modelmentioning

confidence: 99%

“…To this end, we examine the ODE system (10), meaning du/dt = −(q react /ε)dv/dt. On the other hand, the second equation in (10)…”

Section: Preliminariesmentioning

confidence: 99%

“…Applications of this model to real-world wildfire scenarios in several specific geographic regions are documented in [4,8,9]. It is also the basis of the spectral algorithm advanced by San Martin and Torres [10,11], but the particular nature of that numerical method is applicable to a constant diffusion coefficient only. An alternative approach to the description of wildfires through partial differential equations, and their numerical solution by explicit methods is provided in [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, although the combustion process is fully turbulent and three-dimensional, most models used for the simulation of wildfire propagation are formulated and eventually solved in two horizontal space dimensions, although some three-dimensional effects, for instance due to variation of topography, are considered. These include, in particular, [1,2,[4][5][6][7][8][9][10][11][12][13]. This simplifaction, especially for large terrains, also reflects limitations in computational resources available.…”

Section: Introductionmentioning

confidence: 99%

“…This simplifaction, especially for large terrains, also reflects limitations in computational resources available. In this context we refer to Tables I and II in [10] for an overview on models, their assumptions, and the corresponding computational treatment. Explicit treatments of the vertical propagation of a forest fire (but on domains of limited horizontal extension) include [18,19]; see also the references cited in these works.…”

Section: Introductionmentioning

confidence: 99%

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Exploring a Convection–Diffusion–Reaction Model of the Propagation of Forest Fires: Computation of Risk Maps for Heterogeneous Environments

et al. 2020

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The propagation of a forest fire can be described by a convection–diffusion–reaction problem in two spatial dimensions, where the unknowns are the local temperature and the portion of fuel consumed as functions of spatial position and time. This model can be solved numerically in an efficient way by a linearly implicit–explicit (IMEX) method to discretize the convection and nonlinear diffusion terms combined with a Strang-type operator splitting to handle the reaction term. This method is applied to several variants of the model with variable, nonlinear diffusion functions, where it turns out that increasing diffusivity (with respect to a given base case) significantly enlarges the portion of fuel burnt within a given time while choosing an equivalent constant diffusivity or a degenerate one produces comparable results for that quantity. In addition, the effect of spatial heterogeneity as described by a variable topography is studied. The variability of topography influences the local velocity and direction of wind. It is demonstrated how this variability affects the direction and speed of propagation of the wildfire and the location and size of the area of fuel consumed. The possibility to solve the base model efficiently is utilized for the computation of so-called risk maps. Here the risk associated with a given position in a sub-area of the computational domain is quantified by the rapidity of consumption of a given amount of fuel by a fire starting in that position. As a result, we obtain that, in comparison with the planar case and under the same wind conditions, the model predicts a higher risk for those areas where both the variability of topography (as expressed by the gradient of its height function) and the wind velocity are influential. In general, numerical simulations show that in all cases the risk map with for a non-planar topography includes areas with a reduced risk as well as such with an enhanced risk as compared to the planar case.

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Section: Summary Of the Mathematical Modelmentioning

confidence: 99%

“…To this end, we examine the ODE system (10), meaning du/dt = −(q react /ε)dv/dt. On the other hand, the second equation in (10)…”

Section: Preliminariesmentioning

confidence: 99%