Mathematics of Flames


Topic: Mathematics of Flames

Speaker: Claude-Michel Brauner

Event date: 11/15/2018

Event time: 8:30 a.m.

Venue: Lecture Hall 204, Building 9

Sponsor: School of Mathematics and Statistics, Institute of Science and Technology

Brief Introduction of the Speaker:

Claude-Michel Brauner graduated from the University of Paris-South in Orsay under the direction of Roger Temam. His research areas include Nonlinear PDEs, modeling, Free Boundary Problems, combustion and flames. After a whole academic career in France, he has become a Professor Emeritus at the University of Bordeaux. He held several visiting positions abroad; in particular he worked for some time as a consultant for Los Alamos National Laboratory (USA). In China, Claude was from 2009 to 2016 Adjunct Professor and High-end Foreign Expert at Xiamen University.  He is currently an International Visiting Professor at the School of Mathematical Sciences of the University of Science and Technology of China (USTC).


The first part will be devoted to a concise introduction to combustion theory and modeling. Flames constitute an intricate physical system involving fluid dynamics and multistep chemical kinetics. Asymptotic methods introduced by the Russian school in the early mid-20th century allow significant simplifications, especially when a thin flame zone is replaced by a free interface, the flame front.  Flame theory has provided a rich range of equations with fascinating mathematical properties, such as the Kuramoto-Sivashinsky equation.

In a second part, I will briefly discuss a couple of recent works: a gas-solid combustion model which generates fingering pattern formation [1];  a two free interface problem with ignition temperature [2-3].

[1]  L. Hu, C.-M Brauner, J. Shen, G.I. Sivashinsky, Modeling and simulation of fingering pattern formation in a combustion model, M3AS, 5(2015), pp. 685-720.

[2]  C.-M Brauner, P. Gordon, W. Zhang, An ignition-temperature model with two free interfaces in premixed flames, Combution Theory Modelling, 20(2016), pp. 976-994. Special issue dedicated to G. I. Sivashinsky.

[3] D. Addona, C.-M. Brauner, L. Lorenzi, W. Zhang, Instabilities in a combustion model with two free interfaces (submitted).