Variational Multiscale Modeling of Lithium Batteries

Abstract

Batteries are required to have higher energy and power density to meet the requirement of future electric vehicles and other power supply applications. To ensure the safety and durability of the high energy lithium batteries, the numerical study is the key to understanding and design of the next generation batteries. More importantly, the modeling and simulation study of lithium batteries help us understand the underlying causes of the electrochemical, electrical, thermal, and mechanical performance of a lithium battery under various operating conditions. However, the traditional modeling method of lithium batteries assumes the homogeneous structure and reaction to reduce the complexity of the model. The heterogeneity of the battery electrodes significantly impacts the performance of a battery. Due to the complex microstructure of the battery electrodes, it requires ultra-fine meshes to model the various length scales of the electrode structure, which requires very high computing power. This high computational cost is not practical for the numerical optimization design and long-term cycling simulations. Therefore, a variational multiscale method (VMM) is the key to model a lithium battery with considering the heterogeneity. The proposed VMM model reduces the computational cost of a realistic 3D battery model without compromise the accuracy of the heterogeneity. The VMM splits the battery model into macro-scale and micro-scale. By applying the micro-green function, which was firstly developed by Hughes [1] and then extended to battery modeling by us [2], as illustrated in Fig. 1, the micro-scale problem is analytically solved through the projection based on the macro-scale solution to obtain more accurate results. By doing so, we can significantly increase the computational efficiency and accuracy of conducting complex battery multi-scale simulations. With this method, we can simulate battery degradations in the realistic microstructure over hundreds of charge and discharge cycles with a reasonable computational cost. With the understanding of the battery behavior over long-term cycling, the battery electrodes can be redesigned to obtain longer lifetime and better performance through the numerical optimization for energy storage applications. [1] T.J. Hughes, G. Sangalli, Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM Journal on Numerical Analysis, 2007. 45(2): p. 539-557. [2] L. Liu, M. Moradi, Towards a More Realistic Battery Model: Variational Multiscale Modeling of Li-Ion Batteries, ECS Transactions, 2017. 77(11): p. 273-291 Figure 1