Multiscale Partial Differential Equation and Finite Element Modelling of Energy Storage Systems Integrating Thermodynamic and Electromagnetic Phenomena for Sustainable Solutions

Abstract

Multiscale PDE-FEM models of energy storage systems combine electromagnetic phenomena with thermodynamic phenomena. They investigate very complicated systems with numerous parameters, beginning with those at the microstructure level of a material and extending to those at the device level. With this method, the simulation is quite detailed and demanding for the design of permanent, efficient energy storage solutions. Multiscale PDE-FEM models of energy storage aim to provide a high-end, multifaceted technique for precision yet uncomplicated simulation of the complex thermodynamic and electromagnetic processes at multiple scales and time scales. This aims to achieve high fidelity and computational ability in selecting design, performance, and durability of energy storage systems, which, through modeling, will facilitate further research into more flexible and durable energy solutions. The multiscale nature of energy storage systems involves different methods of modeling on various scales, which are the principal methods to be considered in multiscale PDE-FEM modeling. This consists of a continuum-scale model (macro-homogeneous, cell-packing level) of the behavior of the entire system, and a microstructure model (pore scale, atomistic) of a broad variety of material properties and events. The combination of these parameters with generalized multiscale finite methods (GMSFEM) and asymmetric multiscale methods (HMM) is necessary to guarantee a realistic representation of thermodynamic and electromagnetic processes, coupled on a strong and permanent basis. The PDE-FEM model with many scales has also reached significant energy storage. They made predictions of accurate coupled thermodynamic and electromagnetic behavior to enhance performance and design long-term designs with service life. These models have identified important mechanisms of failure at the microstructural scale by bridging scales, providing information to develop a more permanent and sustainable energy solution.