Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach


Authors: Ekeoma R. Ijioma and Adrian Muntean
Journal: Quart. Appl. Math.
MSC (2010): Primary 80A32, 76M50; Secondary 80A25, 35B27
DOI: https://doi.org/10.1090/qam/1509
Published electronically: June 19, 2018
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Abstract: We target the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of a coupled system of evolution equations pertinent to filtration combustion.


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Additional Information

Ekeoma R. Ijioma
Affiliation: MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland
Address at time of publication: University of Limerick, Castletroy, Limerick, V94 T9PX.
Email: e.r.ijioma@gmail.com

Adrian Muntean
Affiliation: Department of Mathematics and Computer Science, Karlstad University, Sweden
Email: adrian.muntean@kau.se

DOI: https://doi.org/10.1090/qam/1509
Keywords: Filtration combustion, thermal dispersion, periodic homogenization, two-scale convergence with drift
Received by editor(s): March 29, 2018
Published electronically: June 19, 2018
Additional Notes: The first author was supported by Science Foundation Ireland (SFI) under Grant Number 14/SP/2750.
The second author was supported by NWO MPE “Theoretical estimates of heat losses in geothermal wells” (Grant Number 657.014.004)
Article copyright: © Copyright 2018 Brown University

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