Harsha Hutridurga

Upscaling nonlinear adsorption in periodic porous media – homogenization approach

We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection–diffusion equations, one in the bulk and one on the pore boundaries, coupled by an exchange reaction term. The novelty of our work is to consider a nonlinear reaction term, a so-called Langmuir isotherm, in an asymptotic regime of strong convection. We therefore generalize previous works on a similar linear model. Under a technical assumption of equal drift velocities in the bulk and on the pore boundaries, we obtain a nonlinear monotone diffusion equation as the homogenized model. Our main technical tool is the method of two-scale convergence with drift.

Convergence Along Mean Flows

We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly oscillating, locally periodic coefficients and

Maxwell–Stefan diffusion asymptotics for gas mixtures in non-isothermal setting

\mathcal{O}(\eps^{-1})

Simultaneous diffusion and homogenization asymptotic for the linear Boltzmann equation

mean convection term. Crucial to our analysis is the introduction of a fast time variable,

Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell–Stefan type

\tau=\frac{t}{\eps}

On the Maxwell–Stefan diffusion limit for a mixture of monatomic gases

, not apparent in the heterogeneous problem. The effective diffusion coefficient is expressed in terms of the average of Eulerian cell solutions along the orbits of the mean flow in the fast time variable. To make this notion rigorous, we use the theory of ergodic algebras with mean value.

On the homogenization of multicomponent transport

Abstract A mathematical model is proposed where the classical Maxwell–Stefan diffusion model for gas mixtures is coupled to an advection-type equation for the temperature of the physical system. This coupled system is derived from first principles in the sense that the starting point of our analysis is a system of Boltzmann equations for gaseous mixtures. We perform an asymptotic analysis on the Boltzmann model under diffuse scaling to arrive at the proposed coupled system.

Cloaking via Mapping for the Heat Equation

This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path

Diffusion limit for Vlasov-Fokker-Planck Equation in bounded domains

\varepsilon

Homogenization of reactive flows in periodic porous media

and the heterogeneity length scale