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We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…

Condensed Matter · Physics 2016-08-15 N. Provatas , T. Ala-Nissila , M. Grant , K. R. Elder , L. Piché

We examine analytically and numerically the evolution of a relativistic fireball. We show that, after an early rearrangement phase, most of the matter and energy in the fireball is concentrated within a narrow shell. The shell propagates at…

Astrophysics · Physics 2015-06-24 Tsvi Piran , Amotz Shemi , Ramesh Narayan

The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. A general method for deriving equations for the flame front position is developed. On the basis of the Thomson circulation theorem…

Fluid Dynamics · Physics 2007-05-23 Kirill A. Kazakov

Sivashinsky's (1977) nonlinear integro-differential equation for the shape of corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem, involving the 2N complex poles of the flame slope. Thual, Frisch & Henon (1985)…

Classical Physics · Physics 2008-12-18 Guy Joulin , Bruno Denet

(Abridged) A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully-resolved premixed flame with a highly subsonic,…

High Energy Astrophysical Phenomena · Physics 2015-01-16 A. Y. Poludnenko

In this work, we study the propagation of wildfires using an advection--diffusion--reaction model which also includes convective and radiative heat loss. An existing model is discussed \cite{asensio_2002} and a physically consistent…

Analysis of PDEs · Mathematics 2025-05-13 Koondanibha Mitra , Qiyao Peng , Cordula Reisch

A hybrid numerical model previously developed for combustion simulations is extended in this article to describe flame propagation and stabilization in porous media. The model, with a special focus on flame/wall interaction processes, is…

Fluid Dynamics · Physics 2023-07-12 S. A. Hosseini , Dominique Thevenin

In this paper we consider a one-dimensional reaction-diffusion model with piecewise continuous reaction term that describes propagation of autoignition fronts in reactive co-flow jets in a certain parametric regime. The model is reduced to…

Analysis of PDEs · Mathematics 2026-03-30 Mingxin Ma , Peter V. Gordon , Robert Roussarie , Peipei Shang , Claude-Michel Brauner

In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…

Analysis of PDEs · Mathematics 2024-02-29 Amanda Matson , Claude-Michel Brauner , Peter V. Gordon

Understanding how intrinsically fast hydrogen-air premixed flames can be rendered much faster in turbulence is crucial for systematically developing hydrogen-based gas turbines and spark ignition engines. Here, we present fundamental…

Fluid Dynamics · Physics 2025-01-30 Yuvraj , Hong G. Im , Swetaprovo Chaudhuri

Preferential diffusion plays a critical role in the evolution of lean premixed hydrogen flames, influencing flame surface corrugation and overall flame behavior. Simulating such flames with tabulated chemistry (TC) methods remains…

The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that…

Fluid Dynamics · Physics 2007-05-23 Kirill A. Kazakov

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…

Fluid Dynamics · Physics 2024-06-28 Joel Daou , Prabakaran Rajamanickam

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level…

Analysis of PDEs · Mathematics 2015-05-19 Yu-Yu Liu , Jack Xin , Yifeng Yu

The current work examines regimes of the hydrogen-oxygen flame propagation and ignition of mixtures heated by radiation emitted from the flame. The gaseous phase is assumed to be transparent for the radiation, while the suspended particles…

Fluid Dynamics · Physics 2015-11-24 Michael A. Liberman M. FIvanov , A. D. Kiverin

Here we perform the first analysis of high-fidelity simulations of the propagation of lean hydrogen flames through porous media, taking cylindrical arrays a representative example geometry. In this fundamental study we discuss the impact of…

Fluid Dynamics · Physics 2025-03-24 H. M. Broadley , S. J. Lind , J. R. C. King

Propagation of turbulent premixed flames influenced by the intrinsic hydrodynamic flame instability (the Darrieus-Landau instability) is considered in a two-dimensional case using the model nonlinear equation proposed recently. The…

Mathematical Physics · Physics 2012-11-27 Maxim Zaytsev , Vitaliy Bychkov

This work presents an experimental set of Bunsen flames characterized by a moderate Reynolds number and a variable turbulence intensity. Ten lean hydrogen-enriched methane-air mixtures at three levels of turbulence are investigated, ranging…

Fluid Dynamics · Physics 2023-12-01 Guido Troiani , Pasquale Eduardo Lapenna , Francesco D'Alessio , Francesco Creta

We study in a strip of $\mathbb R^2$ a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter…

Analysis of PDEs · Mathematics 2018-07-09 Davide Addona , Claude-Michel Brauner , Luca Lorenzi , Wen Zhang

Large-eddy simulations (LES) of a planar turbulent lean hydrogen-air jet flame at Re = 11000 are performed using a tabulated flamelet model based on mixture-averaged diffusion that incorporates detailed transport, including differential and…