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We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…
In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not…
The stability of a magnetic deflagration front in a collection of molecular magnets, such as Mn_12-acetate, is considered. It is demonstrated that stationary deflagration is unstable with respect to one-dimensional perturbations if the…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
Steady premixed flames subjected to space-periodic steady forcing are studied via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For both, the flame slope is posited to comprise contributions from complex poles to…
I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for…
A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is…
In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is…
We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…
The stabilization mechanisms of fully premixed NH3/H2/air flames anchored behind a bluff body are investigated using combined experiments and direct numerical simulations. Particular attention is given to the interplay between preferential…
We first briefly recall the basic mechanisms controlling the hydrodynamic and thermo-diffusive stability of planar laminar premixed flames, and give the state of the theoretical analysis. We then describe some novel experiments to observe…
Direct interactions between the flow field and the chemical reaction in premixed flames occur when the reaction zone thickness is comparable to, or greater than flow length scales. To study such interactions, a laminar model is considered…
We use a set of cosmological simulations combined with radiative transfer calculations to investigate the distribution of neutral hydrogen in the post-reionization Universe. We assess the contributions from the metagalactic ionizing…
In this paper we study the stability of fronts in a reduction of a well-known PDE system that is used to model the combustion in hydraulically resistant porous media. More precisely, we consider the original PDE system under the assumption…
We study front speeds of curvature and strain G-equations arising in turbulent combustion. These G-equations are Hamilton-Jacobi type level set partial differential equations (PDEs) with non-coercive Hamiltonians and degenerate nonlinear…
The paper aims at assessing a hypothesis that resolution required to evaluate fuel consumption and heat release rates by directly (i.e., without a subgrid model of unresolved influence of small-scale turbulent eddies on the local flame)…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with…
The fractal scaling properties of turbulent premixed flame fronts have been investigated and considered for modelling sub-grid scales in the Large-Eddy-Simulation framework. Since the width of such thin reaction fronts cannot be resolved…
The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…
We present a numerical model which allows us to investigate thermonuclear flames in Type Ia supernova explosions. The model is based on a finite-volume explicit hydrodynamics solver employing PPM. Using the level-set technique combined with…