Phase-field models for Li-metal batteries

A convergent, non-oscillatory, efficient algorithm and code for predicting shape changes in lithium metal batteries using phase-field models

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well documented in the literature. In this paper, using a motivating example of a moving boundary model in one and two-dimensions, we show how one can formulate phase-field models, implement algorithms for the same and analyze the results. An open-access code with no restrictions is provided as well. The article concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth.

Two-Dimensional Model

MAPLE

Open Maple, and use “Maple input” in the display option.
One-dimensional Maple code is not optimized or compiled to improve the speed.

- UMFPACK Solver

05/28/2022 Maple (PDF)

: Calls the sparse jacobian in vector format and enables compiled call for both the residues and the sparse entries of the Jacobian.

05/02/2022 Maple (PDF)

: Directly calls MatVecSolve in UMFPACK and reduces overhead calls for LinearSolve.

04/18/2022 Maple (PDF)

: Uses LinearSolve function in maple.

- PARDISO Solver

04/23/2022 Maple (PDF)

: Updated to use CodeTools:-Usage to report cpu time and memory usage.

04/21/2022 Maple (PDF)

: Uses compiled PARDISO solver in dynamic link library for maple.

COMSOL

This code requires electrochemistry and electrodeposition modules.

MATLAB

One-dimensional Maple and MATLAB codes will be posted soon.