Residual Based Error Estimator for Chemical-Mechanically Coupled Battery Active Particles

TL;DR

This paper develops and compares residual-based, Kelly, and gradient recovery adaptive finite element error estimators for simulating chemo-mechanical coupling in lithium-ion battery particles, highlighting the effectiveness of residual-based estimation.

Contribution

It introduces a residual-based error estimator explicitly derived for complex chemo-mechanical battery models and compares its performance with other estimators in 3D simulations.

Findings

Residual estimator depends strongly on cell error component.

Gradient recovery estimator captures lithium flux changes effectively.

Kelly estimator tends to overestimate error.

Abstract

Adaptive finite element methods are a powerful tool to obtain numerical simulation results in a reasonable time. Due to complex chemical and mechanical couplings in lithium-ion batteries, numerical simulations are very helpful to investigate promising new battery active materials such as amorphous silicon featuring a higher energy density than graphite. Based on a thermodynamically consistent continuum model with large deformation and chemo-mechanically coupled approach, we compare three different spatial adaptive refinement strategies: Kelly-, gradient recovery- and residual based error estimation. For the residual based case, the strong formulation of the residual is explicitly derived. With amorphous silicon as example material, we investigate two 3D representative host particle geometries, reduced with symmetry assumptions to a 1D unit interval and a 2D elliptical domain. Our numerical studies show that the Kelly estimator overestimates the error, whereas the gradient recovery estimator leads to lower refinement levels and a good capture of the change of the lithium flux. The residual based error estimator reveals a strong dependency on the cell error part which can be improved by a more suitable choice of constants to be more efficient. In a 2D domain, the concentration has a larger influence on the mesh distribution than the Cauchy stress.