Formal Equivalence between Doyle–Fuller–Newman and Dual-Continuum Lithium-Ion Battery Models

Abstract Upscaled electrochemical models are widely used to simulate lithium-ion batteries efficiently, with the Doyle–Fuller–Newman (DFN, or P2D) model serving as the standard framework. Recently, dual-continuum (DC) models have emerged as an alternative – these avoid simplifying assumptions on particle geometry through a closure problem that is solved on the true microstructure. On the surface, the DFN and DC models appear starkly different. However, in this work we demonstrate that they are formally equivalent when: (i) active-material particles are isolated spheres of uniform radius, (ii) the 'transient' DC formulation is used, (iii) initial concentration is uniform, and (iv) diffusivity does not depend on radial position. A similar equivalence exists between single-particle and single-continuum models. This equivalence provides fundamental insight into both approaches: the DC model reduces exactly to the DFN for idealised spherical geometries while enabling simulation of arbitrarily complex microstructures through closure problems. We validate this equivalence through simulations and discuss implications for developing efficient battery models, particularly regarding the time convolution describing memory effects in diffusion processes.