A Segregated Approach for Modeling the Electrochemistry in the 3-D Microstructure of Li-Ion Batteries and Its Acceleration Using Block Preconditioners

Abstract

Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

MATBOX: An Open-source Microstructure Analysis Toolbox for microstructure generation, segmentation, characterization, visualization, correlation, and meshing

“…Once segmented, the electrode microstructure is characterized (i.e., microstructure parameters relevant to the application are calculated). While suitable for design guidance and being fairly successive to match experimental data [2,7], these models are intrinsically restricted by their macroscale approach and microstructure simplification [8]. To remedy these limitations, microscale models [8][9][10][11][12][13][14] are explicitly solving the system of equations directly on the microstructure geometry, removing both microstructure assumptions and parameters.…”

“…While suitable for design guidance and being fairly successive to match experimental data [2,7], these models are intrinsically restricted by their macroscale approach and microstructure simplification [8]. To remedy these limitations, microscale models [8][9][10][11][12][13][14] are explicitly solving the system of equations directly on the microstructure geometry, removing both microstructure assumptions and parameters. Microscale models are especially relevant to investigate impact of microstructure heterogeneities and local features (e.g., cracks) otherwise neglected by their macroscale counterpart on electrochemical performances, although at the price of a much higher CPU and RAM cost.…”

“…Furthermore, to enable wide design space analysis and complement imaging capabilities, microstructure generation algorithms are also included (both active material and additive phases) in the toolbox. This toolbox has been used for characterizing LIB electrode microstructures in previous works [1,15,16], and for providing full cell meshes for microscale electrochemical LIB model [8]. Fig.…”

“…Meshes can be generated for the whole volume (i.e., a unique mesh), for groups of phases (e.g., a first mesh for the union of positive current collector and cathode solid material, a second mesh for the union of separator and electrolyte within both electrodes, and a third mesh for the union of negative current collector and anode solid material), and for each phase, with meshes having conforming interfaces. The above choice depends on the modelling method: a monolithic model would require a single mesh for the whole volume, while a segregated model [8] -that solves domain sequentially -would need meshes per phase or per group of phases. The latter would use the conforming interfaces to transfer information between meshes.…”

“…The module contains mesh quality calculation, mesh visualizations, and mesh export/conversions (.mat, .csv, .msh, .inp, .stl) using Iso2mesh built-in functions. The .mat and .csv files contain vertices coordinates, cell connectivities, and cell phase labels required to re-build from scratch meshes in a FEM software, as did with FEniCS [34] in a previous work [8], while the other file extensions can be used to import directly the as-generated meshes in software that support them (e.g. Abaqus).…”