A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models

Jinyong Kim, Anudeep Mallarapu, Shriram Santhanagopalan, John Newman

Research output: Contribution to journalArticlepeer-review

4 Scopus Citations


Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

Original languageAmerican English
Article number232413
Number of pages14
JournalJournal of Power Sources
StatePublished - 1 Feb 2023

Bibliographical note

Publisher Copyright:
© 2022

NREL Publication Number

  • NREL/JA-5700-84903


  • Battery modeling
  • Battery solver
  • Fast charging
  • Numerical algorithm
  • Pseudo-two-dimensional model
  • Solid-state diffusion


Dive into the research topics of 'A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models'. Together they form a unique fingerprint.

Cite this