Numerical Model Reduction of Multi‐Scale Electrochemical Ion Transport

ABSTRACT In this paper, we develop a Numerical Model Reduction (NMR) framework for multi‐scale modeling of electro‐chemically coupled ion transport. Upon introducing the governing equations and employing Variationally Consistent Homogenization, a two‐scale model, consisting of a macro‐scale and a sub‐scale part, is obtained. Instead of solving for the computationally expensive FE 2 simulation, where the macro‐scale and sub‐scale problems are solved in a nested fashion, we exploit NMR by training a surrogate model that replaces the sub‐scale finite element simulations. The surrogate model is trained by performing Proper Orthogonal Decomposition on snapshots of the primary fields. Each macro‐scale quadrature point is no longer occupied by a Representative Volume Element simulation; instead, it is replaced by a surrogate model that consists of a system of Ordinary Differential Equations. In this way, a computationally efficient solution scheme for solving two‐scale problems is obtained.