Existing battery modeling works have limitations in addressing the dependence of transport properties on local field variations and characterizing the response of anisotropic media.

These limitations are tackled by means of a nested finite element (FE2) multiscale framework in which microscale simulations are employed to comprehensively characterize an anisotropic medium (macroscale).

The approach is applied to the numerical simulation of transport processes in lithium ion battery separators.

From the microscale solution, homogenized fluxes and their dependence on the downscaled macroscale variables are upscaled, thereby replacing otherwise assumed macroscale constitutive laws.

The tensorial nature of macroscale effective transport properties stems from the numerical treatment.

The proposed approach is verified against full-scale simulations. Several numerical examples are used to demonstrate the perils associated with accepted procedures, leading in some cases to severe discrepancies in the prediction of field quantities (from differences in the potential drop across the separator of about 27% for a fixed microstructure to more than 100% in the case of an evolving microstructure). Despite the use of simplified assumptions (e.g., synthetic microstructures), the numerical results demonstrate the importance of a tensorial description of transport properties in the modeling of battery processes.