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Free interface problems arising in premixed flame propagation

Abstract: 

In combustion theory, the propagation of premixed flames is usually described by the conventional thermal-diffusional model with standard Arrhenius kinetics. Formal asymptotic methods based on large activation energy have allowed simpler descriptions, especially when the thin flame zone is replaced by a free interface, called the flame front, which separates burned and unburned gases. At the flame front, the temperature and mass fraction gradients are discontinuous.

Models describing dynamics of thick flames with stepwise ignition-temperature kinetics have recently received considerable attention. There are differences with the Arrhenius kinetics, for example in the case of zero-order stepwise kinetics there are two free interfaces. At the free interface(s), the temperature and mass fraction gradients are this time continuous.

Both classes of free interface problems (Arrhenius and ignition-temperature kinetics) are a priori not classical Stefan problems, as there is no specific condition on the velocity of the interface(s). However, at least near planar traveling fronts, we are able to associate the velocity to a combination of spatial derivatives up to the second order (second-order Stefan condition). Then, we may reformulate the systems as fully nonlinear problems which are very suitable for stability analysis and numerical simulation.


Short Bio

Claude-Michel Brauner graduated from Paris-Sud University in Orsay under the direction of Roger Temam. His research areas include nonlinear PDEs, Free Boundary Problems and instabilities of fronts, modeling for combustion and flames, HIV. Following an academic career in France, he became a Professor Emeritus at the University of Bordeaux. Furthermore, he has held several visiting positions in Europe and the United States, including a ten-year consultant position for the Los Alamos National Laboratory. In China, from 2009 to 2017, Claude was Adjunct Professor at Xiamen University. He is currently a full-time visiting professor at the School of Mathematical Sciences in the University of Science and Technology of China (USTC) in Hefei.