Shu Xu, Doctor, Peking University

Liqun Cao, Professor

Optimal-rate finite element error estimates and a twice decoupled solver for the Doyle-Fuller-Newman model of lithium-ion cells

14:30-16:00 December 12 (Friday), N213

The Doyle-Fuller-Newman (DFN) model, commonly referred to as the pseudo-two-dimensional (P2D) model when the cell region is simplified to one dimension, is the most widely used physics-based model for lithium-ion cells. It is essential in various engineering applications, including estimating the state of charge (SOC), analyzing capacity performance, and generating impedance spectra. Furthermore, as a cornerstone of battery modeling, it provides a foundation for incorporating additional physics, enabling various model extensions.

In the first part of this talk, we present a finite element error analysis of the DFN model. Central to our approach is a novel projection operator designed for the pseudo-(N+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions 2≤N≤3 and achieve optimal convergence rates of h+(\Delta r)^2. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, our error analysis can also be extended beyond isothermal conditions.

The second part proposes a novel solver that fully decouples the microscopic variable through two effective decoupling procedures, along with an optional decomposition strategy. These approaches significantly accelerate the solution process while maintaining low memory overhead, making the solver particularly suitable for large-scale 2D/3D problems. Numerical experiments with realistic battery parameters demonstrate the significantly superior performance of the proposed solver over existing solvers.