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Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

P. Gordon — 2010

Mathematical Modelling of Natural Phenomena

Gaseous detonation is a phenomenon with very complicated dynamics which has been studied extensively by physicists, mathematicians and engineers for many years. Despite many efforts the problem is far from a complete resolution. Recently the theory of subsonic detonation that occurs in highly resistant porous media was proposed in [4]. This theory provides a model which is realistic, rich and suitable for a mathematical study. In particular, the model is capable of describing the transition from...

A Reduced Model for Flame-Flow Interaction

P. Gordon;  M. Frankel;  G. Sivashinsky — 2010

Mathematical Modelling of Natural Phenomena

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...

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