Variational Multiscale Modeling of Charge Transport in Li Metal Battery

Abstract

Battery performance highly depends on charge transport phenomena. The length scale of battery charge transport modeling is from nanometers to millimeters, therefore it makes the computational modeling difficult to accomplish. Moreover, the charge transport is well known at macro-scale and is easy to examine but there is difficulty in understanding the phenomena at micro-scale. Hence there is need for a framework that not only predicts the performance at macro-scale but also couples micro-scale details (e.g., microstructure and electrochemical reactions). The variational multiscale method (VMM) can be utilized as a paradigm for deriving models and numerical methods capable of dealing with multiscale charge transport phenomena [1]. The VMM can be applied to a broad range of problems and applications like complex electrochemical systems (e.g., Lithium batteries). VMM modeling is one of the essential tools to ascertain varied features of a problem concerning multiscale charge transport phenomena. In addition, VMM can be utilized to investigate continuum-scale systems with tracking detailed, electrochemical dynamics at the micro-scale [2]. Thus developing a VMM modeling framework to investigate the aforementioned problem is of much importance for obtaining reliable computational simulation results. We will focus on building a link between battery micro-scale details and battery continuum level performance via VMM. The basic idea is to decompose the battery electrochemical modeling ODE/PDE solutions into two separate solutions including fine and coarse scale contributions. Fine scale equations will be solved with regard to coarse scale residuals and then the solution will be eliminated from coarse scale equations. Consequently, modified coarse scale equations which include the effects of fine scale can be obtained [3]. We will validate our model against Li metal batteries experimental studies on charge transport. Employing VMM, we can obtain charge transport at different levels and we expect the simulation and experimental data show better accuracy than traditional continue level simulations. Reference [1] T.J.R. Hughes, G.R. Feijόo, L. Mazzei, J. Quincy, Computer Methods in Applied Mechanics and Engineering, 3-24, 166 (1998) [2] S. Lee, The University of Michigan, 2011 [3] M.G. Larson, A. Målqvist, Computer Methods in Applied Mechanics and Engineering, 2313-2324, 196 (2007)