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

TL;DR

This paper develops a periodic homogenization method using two-scale convergence with drift to analyze a nonlinear reaction-diffusion-convection system modeling filtration combustion with fast drift effects.

Contribution

It introduces a novel homogenization approach for nonlinear filtration combustion systems considering fast drift effects and heterogeneity.

Findings

Derived upscaled combustion equations with effective parameters.

Handled nonlinearity of surface reactions in homogenization.

Provided a framework for analyzing heterogenous filtration combustion systems.

Abstract

We target at the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts affect the competition between heat and mass transfer processes as well as the interplay between the surface nonlinear chemical reactions and the transport processes. To handle 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 combustion equations together with the effective transport and reaction parameters. The main difficulty here is to treat the case of the system combined with the nonlinearity of the surface production.