A Computationally Efficient Approach for the Simulation of Silicon Anodes in Lithium-Ion Cells

Abstract

Silicon has emerged as a frontrunner for next generation anode materials due to its high theoretical gravimetric capacity (∼4200 mAh g-1). The presence of volume changes and stress in silicon anodes introduces strong, nonlinear couplings with the lithiation and delithiation process, requiring a significant increase in the complexity of the mathematical framework describing its behavior. A mathematical description of the multiphysics coupling process is presented, requiring the simultaneous solution of the spherical diffusion equations for a binary system with volume change and stress applied to a representative particle. The resulting model description is in the form of a nonlinear set of index-2 Partial Differential and Algebraic Equations (PDAEs). This paper proposes a computationally efficient approach to solve the PDAE system, with the objective of predicting the lithium concentration, volume change, and stress generation during galvanostatic charge and discharge conditions. A semi-explicit scheme is proposed to reformulate the original system into decoupled sets of nonlinear ordinary differential equations and nonlinear algebraic equations. After a grid sensitivity analysis in the space and time domains, the proposed approach results into a computationally efficient implementation that ensures the numerical accuracy in solving this problem, for use in lithium-ion battery control and estimation applications. This study shows that a semi-explicit scheme can produce results at a rate 2.5–3.5 times faster with comparable accuracy when compared to traditional fully implicit solution methods. Limiting the number of Newton iterations in the semi-explicit scheme further reduces the semi-explicit computation time by 25 minutes.