Geodesic
A Reduced Model for Flame-Flow Interaction
P. Gordon1 ; M. Frankel2 ; G. Sivashinsky3
1 Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
2 Department of Mathematical Sciences, Indiana University Purdue University, Indianapolis, IN 46202, USA
3 Department of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 2, pp. 1-12

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The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order dynamic equations for the flame interface and its temperature. As an illustration the new model is applied for description of diffusively unstable stagnation-point flow flames.
DOI : 10.1051/mmnp:2008015

P. Gordon 1 ; M. Frankel 2 ; G. Sivashinsky 3

1 Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
2 Department of Mathematical Sciences, Indiana University Purdue University, Indianapolis, IN 46202, USA
3 Department of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
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P. Gordon; M. Frankel; G. Sivashinsky. A Reduced Model for Flame-Flow Interaction. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 2, pp. 1-12. doi: 10.1051/mmnp:2008015

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