Lectures on Mathematical Combustion

Buckmaster, J.; Ludford, G. S. S.

doi:10.1137/1.9781611970272

Cited by 104 publications

(55 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (1.1) arises in models of equidiffusional premixed Bunsen flames. The function u is a normalized temperature and its level sets represent the profile of a conical-shaped Bunsen flame coming out of a thin elongated Bunsen burner (see Buckmaster and Ludford [12], Joulin [24], Sivashinsky [38], Williams [40]). The temperature of the unburnt gases is close to 0 and that of the burnt gases is close to 1, the hot zone being above the fresh zone.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability of travelling waves in a model for conical flames in two space dimensions

Hamel

Monneau

Roquejoffre

2004

Annales Scientifiques de l’École Normale Supérieure

View full text Add to dashboard Cite

Abstract. This paper deals with the question of the stability of conical-shaped solutions of a class of reaction-diffusion equations in IR 2 . One first proves the existence of travelling waves solutions with conical-shaped level sets, generalizing earlier results by Bonnet, Hamel and Monneau [9], [19]. One then gives a characterization of the global attractor of these semilinear parabolic equations under some conical asymptotic conditions. Lastly, the global stability of the travelling waves solutions is proved.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability of travelling waves in a model for conical flames in two space dimensions

Hamel

Monneau

Roquejoffre

2004

Annales Scientifiques de l’École Normale Supérieure

View full text Add to dashboard Cite

show abstract

“…1 It is equal here to each side of Equation (13). The quantity S represents the flame speed or burning velocity defined as the speed with which the flame travels with respect to the unburnt gas ahead of it (or more precisely just ahead of its reaction sheet 2 ), or equivalently, as minus the speed of the unburnt gas at r = R + with respect to the stationary flame ball, this speed being obviously given by the right-hand side of (15).…”

Section: Notation and Preliminary Remarksmentioning

confidence: 99%

Generalized flame balls

Daou

Al-Malki

Ronney

2009

Combustion Theory and Modelling

View full text Add to dashboard Cite

We consider generalized flame balls which correspond to stationary spherical flames with a flow of hot inert gas, either a source or a sink, at the origin. Depending on the flow, these flames can have positive, zero, or negative burning speeds, with zero speeds characterizing the Zeldovich flame balls. A full analytical description of these structures and their stability to radial perturbations is provided, using a large activation energy asymptotic approach and a thermo-diffusive approximation. The results are also complemented by a numerical study. The number and stability of the generalized flame balls are identified in various regions of the l-M-h 0 space, where l is the (reduced) Lewis number, and M and h 0 the flow rate and its enthalpy at the origin, respectively. It is typically found that, when the flow is a source, there is a maximum value of the flow rate M max depending on l and h 0 , above which no stationary solutions exist, and below which there are two solutions characterizing a small stable flame ball and a large unstable flame ball; the implications of these results to the problem of ignition by a hot inert gas stream are discussed. When the flow is a sink, however, there is typically a single unstable solution, except for sufficiently large values of the Lewis number and large negative values of M, where three flame balls exist, the medium one being stable. Finally, the relation between the flame speed, positive or negative, and the flame curvature, small or large, is discussed.

show abstract

“…Because these equations arise in diverse fields of application [10,11,70,71,78,88,93,100,123,201,211,244] such as heat transfer [74,283,284], combustion [31,55,56,99,282], reaction chemistry [13,14], fluid dynamics [54], plasma physics [44,62], soil-moisture physics [30,64,219,248], foam drainage [264,275], crystal growth [127,249], biological population genetics [53,149,155,189,191,192,203], cellular ecology [240], neurology [238] and synergetics [140], the underlying interests and treatment are often different. [98,265] u t = u xx + u (1 − u) which is the archetypical deterministic model for the spread of an advantageous gene in a population of diploid individuals living in a one-dimensional habitat, and its...…”

Section: Introductionmentioning

confidence: 99%

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Gilding¹,

Kersner²

2004

166

View full text Add to dashboard Cite

The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this correspondence unifies and generalizes previous results on the occurrence of travelling-wave solutions of such partial differential equations. The detailed comparison with earlier results simultaneously provides a survey of the topic. It covers travelling-wave solutions of generalizations of the Fisher, Newell-Whitehead, Zeldovich, KPP and Nagumo equations, the Burgers and nonlinear Fokker-Planck equations, and extensions of the porous media equation.

show abstract

Lectures on Mathematical Combustion

Cited by 104 publications

References 0 publications

Stability of travelling waves in a model for conical flames in two space dimensions

Stability of travelling waves in a model for conical flames in two space dimensions

Generalized flame balls

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Contact Info

Product

Resources

About