Investigation of projection-based model-reduction techniques for solid-phase diffusion in Li-ion batteries

In this work, we apply the projection-based model-reduction framework for PDEs of [1] to the diffusion process governing the intercalation of lithium ions into spherical particles that appears in electrochemical models of Li-ion batteries. We first invoke the projection framework with different projections (the so-called natural—i.e. Galerkin—and volume-averaging projections—NP and VAP, respectively) and different basis sets (even monomials and eigenfunctions of the PDE) to arrive at different reduced models, which we then benchmark in a dimensionless frequency-domain setting. Surprisingly, we find that VAP of an even monomial basis yields an unstable reduced model for anything but the lowest order; however, NP yields suitable results for the basis sets and orders considered. Furthermore, we find that the NP-eigenfunction combination makes for a slow convergence when compared to NP with even monomials; however, room for further improvement is seen when compared with a balanced truncation, which is not applicable in the nonlinear setting of concentration-dependent diffusivity.