Non-classical phase transitions at a sonic point.
Nonlinear Time-Fractional Differential Equations in Combustion Science
MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion...
Non-trapping sets and Huygens principle
Non-Trapping sets and Huygens Principle
We consider the evolution of a set according to the Huygens principle: i.e. the domain at time t>0, Λt, is the set of the points whose distance from Λ is lower than t. We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of t, and we give an algorithm to approximate the evolution. Finally we restrict...
Numerical simulation of a point-source initiated flame ball with heat losses
This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.
Numerical simulation of a point-source initiated flame ball with heat losses
This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.
Numerical study of flame propagation in boundary layers.