## Preprint 2020-22

## Raimund Bürger, Elvis Gavilán, Daniel Inzunza, Pep Mulet, Luis M. Villada:

### Exploring a convection-diffusion-reaction model of the propagation of forest fires: computation of risk maps for heterogeneous environments

### Abstract:

The propagation of a forest fire can be described by a convection-diffusion-reaction problem in two space 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. 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 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.

This preprint gave rise to the following definitive publication(s):

**Raimund BüRGER, Elvis GAVILáN, Daniel INZUNZA, Pep MULET, Luis M. VILLADA: ***Exploring a convection-diffusion-reaction model of the propagation of forest fires: computation of risk maps for heterogeneous environments*. Mathematics, vol. 8, 10, article: 1674 (20pp), (2020).