Claude-Michel Brauner

Mathematical modeling in combustion and related topics

Reminiscences on the Life and Work of G.S.S. Ludford.- I : Invited Lectures.- A Nonlinear Elliptic Problem Describing the Propagation of a Curved Premixed Flame.- Mathematical Modeling in the Age of Computing : Is it redundant ?.- Combustion and Compressibility in Gases.- Cool Flame Propagation.- Modeling the Chemistry in Flames.- Computer Simulation of 2D/3D Reacting Flows in Complicately Shaped Regions for Engineering.- Radiative Transfer in Unsteady, Weakly Curved, Particle-Laden Flames.- Numerical Simulation of Coherent Structures in Free Shear Flows.- Diffusion Flame Attachment and flame front propagation along mixing layers.- Some Remarks on Turbulent Combustion from the Attractor Point of View.- Grid Requirements Due to the Inner Structure of Premixed Hydrocarbon Flames.- Nonlinear Studies of Low-Frequency Combustion Instabilities.- Nonlinear Effects of Blow Up and Localization Processes in Burning Problems.- Remarks on the Stability Analysis of Reactive Flows.- Experiments with Premixed Flames.- Solution of Two-Dimensional Axisymmetric Laminar Diffusion Flames by Adaptive Boundary Value Methods.- Shock Induced Thermal Explosion.- Influences of Detailed Chemistry on Asymptotic Approximations for Flame Structure.- II : Shorter Papers.- Numerical Study of Particle-Laden Jets: A Lagrangian Approach.- Mathematical Modelisation of Enclosed Combustion at Constant or Variable Pressure by Vibe Law.- Experimental and Numerical Study of a Heated Turbulent Round Jet.- Interet des Methodes de Calculs en Combustion dans le Developpement des Foyers de Turboreacteurs.- Characterizing Self-Similar Blow-Up.- Some Finite-Element Investigations of Stiff Combustion Problems : Mesh Adaption and Implicit Time-Stepping.- Modeling of Turbulent Diffusion Flames with Detailed Chemistry.- Kinetic Modelling of Light Hydrocarbons Combustion.- Application de Methodes Variationnelles a une Combustion Turbulente Premelangee, Homogene et Stationnaire.- A Minimal Model for Turbulent Flame Fronts.- A Theoretical Study of Air-Solid Two-Phase Flows.- Dynamic Transition of a Self-Igniting Region.- Numerical Model for Turbulent Reactive Flows with Swirl.- Experimental Analysis on the Stability of an Oblique Flame Front.- Vector Computers and Complex Chemistry Combustion.- Numerical Model for Propellant Grain Burning Surface Recession.- Global Existence of Solutions for a Problem in Dynamics of Thermal Explosions.- Elements Finis Autoadaptatifs a Multimaillages pour le Calcul de Vitesses de Flamme.- Flammes minces et interfaces.- Second Order Remeshing Method in 2D Lagrangian Fluid Dynamics.- On Numerical Analysis of Two-Dimensional, Axisymmetric, Laminar Jet Diffusion Flames.- An Algorithm for Allocation and Temperature, and its Consequences for the Chemistry of H2-O2 Combustion.- Existence and Stability in a Plane Premixed Flame Problem.- Computation of Turbulent Diffusion and Premixed Flames with Radiation.

A critical case of stability in a free boundary problem

Abstract. We study the stability of the planar travelling wave solution to a free boundary problem for the heat equation in the whole

Weakly nonlinear asymptotics of the kappa-theta model for cellular flames: the Q-S equation.

\Bbb R^2

Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem

. We turn the problem into a fully nonlinear parabolic system and establish a stability result which is the proper generalization of the one-dimensional case. The curvature terms contribute a gradient squared corresponding to critical growth. The latter is eliminated by means of the Hopf-Cole transformation.

Multi-dimensional stability analysis of planar travelling waves

We consider a quasi-steady version of the κ-θ model of flame front dynamics introduced in [FGS03]. In this case the mathematical model reduces to a single integro-differential equation. We show that a periodic problem for the latter equation is globally well-posed in Sobolev spaces of periodic functions. We prove that near the instability threshold the solutions of the equation are arbitrarily close to these of the Kuramoto–Sivashinsky equation on a fixed time interval if the evolution starts from close configurations. We present numerical simulations that illustrate the theoretical results, and also demonstrate the ability of the quasi-steady equation to generate chaotic cellular dynamics.

Modeling and simulation of fingering pattern formation in a combustion model

We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative effects due to the presence of dust account for the divergence of the radiative flux entering the equation for temperature. This flux is modelled by the Eddington equation. In an appropriate limit the divergence of the flux takes the form of a nonlinear heat loss term. The resulting reduced model is able to capture a hysteresis effect that appears if the amount of fuel in front of the flame, or equivalently, the adiabatic temperature is taken as a control parameter.

Rigorous derivation of the Kuramoto–Sivashinsky equation from a 2D weakly nonlinear Stefan problem

Abstract We describe a method for determining the stability properties of the travelling wave solutions to certain free boundary problems under multi-dimensional perturbations.

THE SPEED LAW FOR HIGHLY RADIATIVE FLAMES IN A GASEOUS MIXTURE WITH LARGE ACTIVATION ENERGY

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G.I. Sivashinsky. Our approach is twofold: (I) we eliminate the front and get to a fully nonlinear system with boundary conditions; (II) we use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations are presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II).

An ignition-temperature model with two free interfaces in premixed flames†

In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter

Instability of the free boundary in a two-dimensional combustion model

\varepsilon