Riemann solutions for counterflow combustion in light porous foam
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The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented.
KeywordsTraveling wave Riemann problem Counterflow combustion Porous medium
Mathematics Subject Classification80A25 35C07 35K57 34C37
The authors would like to thank Prof. S. Schecter and Prof. D. Marchesin for the preliminary work. We also would like to thank Prof. D. Tadeu, I. Ledoino and D. L. de Albuquerque for developing and improving the numerical code RCD used in this work. We thank anonymous referee for help in improving this text.
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