High-order adaptive multi-domain time integration scheme for microscale lithium-ion batteries simulations

TL;DR

The paper tackles microscale lithium-ion battery simulations, where two coupled domains (electrolyte and solid) evolve on very different time scales. It casts the 1D half-cell problem as a system of index-1 semi-explicit DAEs after spatial discretization and introduces a high-order adaptive multi-domain time integration scheme that decouples the subdomains while allowing high-order accuracy through polynomial-in-time coupling of interface variables. The authors develop and analyze explicit and implicit coupling strategies, derive an adaptive coupling timestep rule ${Δt_{c,opt}}$ based on a coupling-error estimate ${ε_p}$ with ${ε_p ≈ α Δt_{c,1}^p}$ and ${Δt_{c,opt} = Δt_{c,1} (tol/ε_p)^{1/p}}$, and demonstrate improved conditioning of subdomain Jacobians versus the fully-coupled system. Validation on a 1D half-cell shows accurate spatial convergence and temporal accuracy, robust performance under oscillatory driving, and potential for scalable 3D simulations with real electrode microstructures. The framework provides a path to high-fidelity, computationally efficient LIB simulations that can incorporate more physics and HPC strategies for large-scale applications.

Abstract

We investigate the modeling and simulation of ionic transport and charge conservation in lithium-ion batteries (LIBs) at the microscale. It is a multiphysics problem that involves a wide range of time scales. The associated computational challenges motivate the investigation of numerical techniques that can decouple the time integration of the governing equations in the liquid electrolyte and the solid phase (active materials and current collectors). First, it is shown that semi-discretization in space of the non-dimensionalized governing equations leads to a system of index-1 semi-explicit differential algebraic equations (DAEs). Then, a new generation of strategies for multi-domain integration is presented, enabling high-order adaptive coupling of both domains in time, with efficient and potentially different domain integrators. They reach a high level of flexibility for real applications, beyond the limitations of multirate methods. A simple 1D LIB half-cell code is implemented as a demonstrator of the new strategy for the simulation of different modes of cell operation. The integration of the decoupled subsystems is performed with high-order accurate implicit nonlinear solvers. The accuracy of the space discretization is assessed by comparing the numerical results to the analytical solutions. Then, temporal convergence studies demonstrate the accuracy of the new multi-domain coupling approach. Finally, the accuracy and computational efficiency of the adaptive coupling strategy are discussed in the light of the conditioning of the decoupled subproblems compared to the one of the fully-coupled problem. This new approach will constitute a key ingredient for the high-fidelity 3D LIB simulations based on actual electrode microstructures.

Figures (18)

• Figure 2.1: Schematic diagram of the 1D LIB half-cell model.
• Figure 2.2: Schematic view of a 1D finite volume grid.
• Figure 2.3: Auxiliary variables introduced at the interfaces $\Gamma_{0}$ and $\Gamma_{am-e}$ for evaluation of the Butler-Volmer current density.
• Figure 4.1: Plots of error vs. $\mathcal{N}_t$ for the multi-domain strategy with coupling at fixed intervals. Errors corresponding to the explicit and implicit coupling are shown with empty black outlined and filled markers, respectively. The dashed lines represent the theoretical accuracy ($\mathcal{O}(\Delta t_c^{p+1})$) for an approximation polynomial of degree $p$.
• Figure 4.2: Plots of the coupling timestep $\Delta t_c$ (s) vs. time $t$ (s) for the multi-domain technique with adaptive coupling. Here $p+1$ is the order of the adaptive coupling. The time-varying (sine wave) applied cell voltage is shown with dashed line.