Étude numérique et asymptotique d'une approche couplée pour la simulation de la propagation de feux de forêt avec l'effet du vent en terrain complexe
The core of this thesis consists in the development of a new coupled model for wildfire spread. This model relies on an atmospheric model based on a single constraint for the wind velocity flow. This constraint given by a divergence equation is derived from a low Mach number approximation. The fire model represents the fireline on the topography as an infinitely thin interface which outlines the burned regions. The level set method allows to track the spread of this interface on the topography.  The fire and atmosphere models are coupled with a source term in the divergence equation governing the wind velocity field. This source is represented as a singular sink-source pair in order to capture the main features of the atmospheric flow near the fireline. Each singularity is supported on an interface, a codimension-2 manifold. The computation of the amplitude of the source term is achieved with Byram's formula for fire intensity. The derivation and particular characteristics of this coupled model are presented in this work.   A regularization technique combined with a rescaling algorithm for a delta function supported on a codimension-2 manifold has been elaborated for this model. A study of the convergence of the solutions of the elliptic problem, associated with the atmospheric model, demonstrates the necessity of this technique to achieve convergence with mesh refinements.  This thesis presents the numerical implementation of the coupled model. The simulations conducted with the model are used to study the fire spread regimes with a dimensionless number obtained in a dimensional analysis. The model is compared to the Firetec model with numerical experiments of fire spread over idealized topographies.
Plume Wildfires Atmosphere Coupled model Fire intensity Heat source Singular interface Delta function Regularization Spread regimes