Comparison of two approaches for treatment of the interface conditions in FV discretization of pore scale models for Li-Ion batteries

Pore scale models of Li-ions transport allow to gain insight into the details of the charge and discharge processes in Li-ion batteries. These models are diffusion type PDE-systems with very complex, nonlinear interface conditions on the interfaces between the active particles in the porous electrodes and the electrolyte. In this work, we discuss two approaches for the treatment of these interface conditions in conjunction with a cell-centered Finite Volume (FV) discretization of the governing equations. The first approach treats exactly the fluxes on the interface, but approximates the Butler-Volmer flux. This approach requires less memory because it does not introduce unknowns on the interface. The second approach introduces unknowns on the interface and discretizes the fluxes, but the Li-ion Butler-Volmer flux is evaluated exactly on the interface. Our numerical results show that the two approaches give very close results when the current rate is low. However, when the current rate becomes higher, the second approach is more accurate than the first one.