(296b) Multi-Scale Coarse-Graining of Diffusion-Convection-Reaction Models

Diffusion, convection and reactions are core phenomena in many disciplines of science and engineering. Due to strong coupling between these processes at various length/time scales, the detailed conservation models (3D transient partial differential equations) can be highly non-linear and can exhibit complex behavior (such as multiple solutions, oscillations, spatial patterns, traveling fronts and regular and irregular spatio-temporal patterns). Exploring these behaviors in multi-dimensional parameter space can be extremely difficult using the detailed models. Reduced order coarse-grained models that eliminate many spatial and/or temporal degrees of freedom are useful in providing a simplified description and engineering analysis of such systems. Historically, such reduced-order (low-dimensional) models are derived by a priori assumptions and based on intuitive approximations. More recent approaches based on the work of Taylor and Aris, volume averaging and center manifold have several short comings when applied to reacting systems. In this talk, I review the work of Prof. Balakotaiah on multi-scale coarse graining of diffusion-convection-reaction (DCR) models using the Lyapunov-Schmidt (L-S) technique and its various extensions in the past twenty years. Specifically, I discuss (i) the conceptual as well as the mathematical aspects of coarse graining of DCR models characterized by multiple time (or length) scales; (ii) how this approach is related to the two main classical concepts of effective transfer and dispersion coefficients used in transport phenomena to describe dispersion phenomena in the literature; and (iii) how to extend the accuracy and range of validity of the multi-scale models using the local position, time, flow and kinetics dependent transfer coefficients. Finally, various applications of the multi-scale multi-mode reduced order models are illustrated. These include real-time simulations of catalytic after-treatment systems, bifurcation and parametric studies of chemical reactors, reactive dissolution of porous media, determination of effective transport properties of multi-phase systems, and developments towards CO₂-constrained energy transition.