Ekeoma R. Ijioma | Searcharxiv

arXiv2018

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

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.

math.AP↗

arXiv2018

Multiscale Galerkin approximation scheme for a system of quasilinear parabolic equations

We discuss a multiscale Galerkin approximation scheme for a system of coupled quasilinear parabolic equations. These equations arise from the upscaling of a pore scale filtration combustion model under the assumptions of large Damkhöler number and small Péclet number. The upscaled model consists of a heat diffusion equation and a mass diffusion equation in the bulk of a macroscopic domain. The associated diffusion tensors are bivariate functions of temperature and concentration and provide the necessary coupling conditions to elliptic-type cell problems. These cell problems are characterized by a reaction-diffusion phenomenon with nonlinear reactions of Arrhenius type at a gas-solid interface. We discuss the wellposedness of the quasilinear system and establish uniform estimates for the finite dimensional approximations. Based on these estimates, the convergence of the approximating sequence is proved. The results of numerical simulations demonstrate, in suitable temperature regimes, the potential of solutions of the upscaled model to mimic those from porous media combustion. Moreover, distinctions are made between the effects of the microscopic reaction-diffusion processes on the macroscopic system of equations and a purely diffusion system.

math.AP↗