Geodesic
A Reduced Model for Flame-Flow Interaction
P. Gordon1 ; M. Frankel2 ; G. Sivashinsky3
1Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
2Department of Mathematical Sciences, Indiana University Purdue University, Indianapolis, IN 46202, USA
3Department 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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