A monolithic, mortar‐based interface coupling and solution scheme for finite element simulations of lithium‐ion cells

Abstract

Summary This work introduces a novel, mortar‐based coupling scheme for electrode‐electrolyte interfaces in 3‐dimensional finite element models for lithium‐ion cells and similar electrochemical systems. The coupling scheme incorporates the widely applied Butler‐Volmer charge transfer kinetics, but conceptually also works for other interface equations. Unlike conventional approaches, the coupling scheme allows flexible mesh generation for the electrode and electrolyte phases with nonmatching meshes at electrode‐electrolyte interfaces. As a result, the desired spatial mesh resolution in each phase and the resulting computational effort can be easily controlled, leading to improved efficiency. All governing equations are solved in a monolithic fashion as a holistic, unified system of linear equations for computational robustness and performance reasons. Consistency and optimal convergence behavior of the coupling scheme are demonstrated in elementary numerical tests, and the discharge of two different realistic lithium‐ion cells, each consisting of an anode, a cathode, and an electrolyte, is also simulated. One of the two cells involves about 1.35 million degrees of freedom and very complex microstructural geometries obtained from X‐ray tomography data. For validation purposes, characteristic numerical results from the literature are reproduced, and the coupling scheme is shown to require considerably fewer degrees of freedom than a standard discretization with matching interface meshes to achieve a similar level of accuracy.

Progress in 3D electrode microstructure modelling for fuel cells and batteries: transport and electrochemical performance

“…Module Aria [78,[140][141][142][143] or NIST Object Oriented Finite Element Analysis program [144] are used as well, while in-house FEM implementations are mainly used to overcome specific limitations of available codes [118].…”

“…This allows flexible and independent grid generation on the two domains: a finer mesh in the solid domain, where strong interfacial gradients in Li concentration are expected due to its low solid diffusivity, and a coarser mesh in the electrolyte domain, where Butler-Volmer interface integrals are evaluated and then fluxes are projected onto the particle side through a discrete interface mapping. Fang et al [118] tested the mortar-based approach up to an interfacial node number ratio of 2.5:1, thus cutting the overall mesh requirements by one third, showing no numerical A c c e p t e d M a n u s c r i p t perturbations at the solid/electrolyte interface and resulting in spatial convergence in the same fashion of conventional matching-node coupling [118].…”

“…Nevertheless, FEM is useful when more physics are simulated together, such as different transport mechanisms occurring in different domains coupled by interfacial (or TPB) charge-transfer kinetics. This is the standard problem simulated in all the microstructure-resolved 3D electrochemical models [98,99,115,116,118,128,132,136,137,139]. Conversely, multiple parallel reaction pathways are seldom considered.…”

A Multi-Physics Battery Model with Particle Scale Resolution of Porosity Evolution Driven by Intercalation Strain and Electrolyte Flow

“…Equations (1), (3), (12), (16)(17), (20), (27) and (28) are coupled and highly nonlinear. Furthermore, the interface conditions, (55a-55b), (57) and (58a-58c) and many coefficients in the partial differential equations depend on the primary variables, introducing further nonlinearity to the system of equations.…”

“…In related work, reconstruction of the microstructure from X-ray tomography data has made simulations on realistic electrodes possible. 17,10,12 We note the work of Wang and Sastry 9 who studied the effective diffusivity and capacity for various idealized, close-packed, as well as experimentally imaged three-dimensional microstructures. Their work, however, neglected any mechanical influences.…”