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# Bourlioux, Anne

Full Professor

Faculty of Arts and Science - Department of Mathematics and Statistics

514 343-5621

### Student supervision Expand allCollapse all

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 Theses and supervised dissertations / 2016-08
Proulx, Louis-Xavier
Abstract
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.

Méthodes rapides et efficaces pour la résolution numérique d'équations de type Hamilton-Jacobi avec application à la simulation de feux de forêt Theses and supervised dissertations / 2015-10
Desfossés Foucault, Alexandre
Abstract
This thesis is divided in three chapters. The first explains how to use the level-set method in a rigorous way in the context of forest fire simulation when the physical propagation model for firespread is Richards' ellipse model. The second chapter presents a new semi-implicit scheme with a proof of convergence for the numerical solution of an anisotropic Hamilton-Jacobi partial differential equation. The advantage of this scheme is it allows the use of approximative solutions as initial conditions which reduces the computation time. The third chapter shows how to use the tools introduced in the first two chapters to study the influence of small-scale variations on the wind speed on firespread using the theory of homogenization.

Approche cartésienne pour le calcul du vent en terrain complexe avec application à la propagation des feux de forêt Theses and supervised dissertations / 2011-01
Proulx, Louis-Xavier
Abstract
The Projection method and Sasaki's variational technique are two methods allowing one to extract a divergence-free vector field from any vector field. From a high altitude wind speed, a velocity field is generated on a staggered grid over a topography given by an analytical function. The Cartesian grid Embedded Boundary method is used for solving a Poisson equation, obtained from the projection, on an irregular domain with mixed boundary conditions. The solution of this equation gives the correction for the initial velocity field to make it such that it satisfies the conservation of mass and takes into account the effects of the terrain. The incompressible velocity field will be used to spread a wildfire over the topography with the Level Set Method. The algorithm is described for the two and three dimensional cases and convergence tests are done.

Modèles de flammelette en combustion turbulente avec extinction et réallumage : étude asymptotique et numérique, estimation d'erreur a posteriori et modélisation adaptative Theses and supervised dissertations / 2011-01
Turbis, Pascal
Abstract
We are interested here in the modeling errors of subgrid flamelet models in nonpremixed turbulent combustion. The goal of this thesis is to develop an a posteriori error estimation strategy to determine the best model within a hierarchy, with a numerical cost at most that of using the models in the first place. Firstly, we develop and test a dual-weighted residual estimator strategy on a system of advection-diffusion-reaction equations. Secondly, we test that methodology on another system of equations, where quenching and ignition effects are added. In the absence of advection, a rigorous asymptotic analysis shows the existence of many combustion regimes already observed in numerical simulations. We obtain approximations of the quenching and ignition parameters, alongside the S-shaped curve, a plot of the maximal flame temperature as a function of the Damköhler number, consisting of three branches and two bends. When advection effects are added, we still obtain a S-shaped curve corresponding to the known combustion regimes. We compare the modeling errors of the asymptotic approximations in the two stable regimes and establish new model hierarchies for each combustion regime. These errors are compared with the estimations obtained by using the error estimation strategy. When only one stable combustion regime exists, the error estimator correctly identifies that regime; when two or more regimes are possible, it gives a systematic way of choosing one regime. For regimes where more than one model is appropriate, the error estimator’s predicted hierarchy is correct.

Simulation numérique de feux de forêt avec réinitialisation et contournement d'obstacles Theses and supervised dissertations / 2010-01
Desfossés Foucault, Alexandre
Abstract
This work presents a forest fire simulation model which uses the Level-Set method. We use a partial differential equation to deform a surface on which our flame front is inscribed. The mathematical foundations of the Level-set method are presented. We then explain a reinitialization method that allows us to treat in a robust way real data and to reduce the calculation time. The effect of the presence of barriers in the fire propagation domain is also studied. Finally, we make an attempt to find the ignition point of a forest fire.

Algorithmes efficaces pour la simulation de gouttes entraînées Theses and supervised dissertations / 2007
Leclaire, Sébastien
Abstract
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Méthode de suivi de front implicite, eulérienne pour un système diphasique bas Mach en une dimension spatiale Theses and supervised dissertations / 2006
Kardhashi, Eva
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Analyse et calibration d'un modèle multiéchelle pour la simulation de feux de forêt Theses and supervised dissertations / 2006
Brunelle, Éric
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Validation des modèles de flammelettes instationnaires en combustion turbulente non-prémélangée Theses and supervised dissertations / 2005
Volkov, Oleg
Abstract
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Extinction d'une flamme prémélangée par un cisaillement : effets instationnaires Theses and supervised dissertations / 2004
Ngouoko, Terence
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Modélisation asymptotique pour la simulation aux grandes échelles de la combustion turbulente prémélangée Theses and supervised dissertations / 2002
Khouider, Boualem
Abstract
Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

### Selected publications Expand allCollapse all

#### Semi-Analytic Validation of a dynamic LES procedure for turbulent premixed flames via the G-equation

BOURLIOUX A., Semi-Analytic Validation of a dynamic LES procedure for turbulent premixed flames via the G-equation Combustion Theory and Modelling, (2012), Àparaître ,

#### A posteriori error estimation for subgrid flamelet models

Bourlioux, Anne, Ern, Alexandre et Turbis, Pascal, A posteriori error estimation for subgrid flamelet models 8, 481--497 (2009), , Multiscale Model. Simul.

#### The effect of wind on the propagation of an idealized forest fire

Babak, Petro, Bourlioux, Anne et Hillen, Thomas, The effect of wind on the propagation of an idealized forest fire 70, 1364--1388 (2009), , SIAM J. Appl. Math.

#### Burning issues with Prometheus---the Canadian wildland fire growth simulation model

Barber, J., Bose, C., Bourlioux, A., Braun, J., Brunelle, E., Garcia, T., Hillen, T. et Ong, B., Burning issues with Prometheus---the Canadian wildland fire growth simulation model 16, 337--378 (2008), , Can. Appl. Math. Q.

#### Symmetry preserving discretization of ${\rm SL}(2,\Bbb R)$ invariant equations

Bourlioux, Anne, Rebelo, Raphaël et Winternitz, Pavel, Symmetry preserving discretization of ${\rm SL}(2,\Bbb R)$ invariant equations 15, 362--372 (2008), , J. Nonlinear Math. Phys.

#### A rigorous asymptotic perspective on the large scale simulations of turbulent premixed flames

Bourlioux, Anne et Khouider, Boualem, A rigorous asymptotic perspective on the large scale simulations of turbulent premixed flames 6, 287--307 (electronic) (2007), , Multiscale Model. Simul.

#### Conditional statistics for a passive scalar with a mean gradient and intermittency

Bourlioux, A., Majda, A. J. et Volkov, O., Conditional statistics for a passive scalar with a mean gradient and intermittency 18, 104102, 10 (2006), , Phys. Fluids

#### Difference schemes with point symmetries and their numerical tests

Bourlioux, A., Cyr-Gagnon, C. et Winternitz, P., Difference schemes with point symmetries and their numerical tests 39, 6877--6896 (2006), , J. Phys. A

#### High-order multi-implicit spectral deferred correction methods for problems of reactive flow

Bourlioux, Anne, Layton, Anita T. et Minion, Michael L., High-order multi-implicit spectral deferred correction methods for problems of reactive flow 189, 651--675 (2003), , J. Comput. Phys.

#### Computing the effective Hamiltonian in the Majda-Souganidis model of turbulent premixed flames

Khouider, Boualem et Bourlioux, Anne, Computing the effective Hamiltonian in the Majda-Souganidis model of turbulent premixed flames 40, 1330--1353 (electronic) (2002), , SIAM J. Numer. Anal.

#### Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

Bourlioux, A. et Majda, A. J., Elementary models with probability distribution function intermittency for passive scalars with a mean gradient 14, 881--897 (2002), , Phys. Fluids

#### Parametrizing the burning speed enhancement by small-scale periodic flows. I. Unsteady shears, flame residence time and bending

Khouider, B., Bourlioux, A. et Majda, A. J., Parametrizing the burning speed enhancement by small-scale periodic flows. I. Unsteady shears, flame residence time and bending 5, 295--318 (2001), , Combust. Theory Model.

#### An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

Bourlioux, A. et Majda, A. J., An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion 4, 189--210 (2000), , Combust. Theory Model.

#### Asymptotic and numerical study of the stabilization of diffusion flames by hot gas

Bourlioux, Anne, Cuenot, Bénédicte et Poinsot, Thierry, Asymptotic and numerical study of the stabilization of diffusion flames by hot gas 120, 143--159 (2000), , Combustion and flame

#### Theoretical and numerical structure of unstable detonations

Bourlioux, Anne et Majda, Andrew J, Theoretical and numerical structure of unstable detonations 350, 29--68 (1995), , Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences

#### Theoretical and numerical structure for unstable two-dimensional detonations

Bourlioux, Anne et Majda, Andrew J, Theoretical and numerical structure for unstable two-dimensional detonations 90, 211--229 (1992), , Combustion and Flame

#### Theoretical and numerical structure for unstable one-dimensional detonations

Bourlioux, Anne, Majda, Andrew J. et Roytburd, Victor, Theoretical and numerical structure for unstable one-dimensional detonations 51, 303--343 (1991), , SIAM J. Appl. Math.

#### Numerical study of unstable detonations

Bourlioux, Anne, Numerical study of unstable detonations Numerical study of unstable detonations, Numerical study of unstable detonations (1991), , Numerical study of unstable detonations