A fast numerical method with non-iterative source term for pseudo-two-dimension lithium-ion battery model

In this work, a fast numerical method with non-iterative volumetric source for pseudo-two-dimensional (P2D) model is proposed for lithium-ion batteries and has been implemented in the open-source software OpenFOAM. The direct determination of the precise potential distribution is enabled by correct boundary conditions derived from the Butler-Volmer equation and charge conservation, due to the mathematical characteristic of the Laplace equation and the small grid scale involved. This method eliminates repeated iterations to obtain the accurate volumetric source distribution for each step required by the sequential full-order model (SFOM) method. The numerical solving boundary conditions coincide with those of the conventional P2D model in terms of physical meaning. Nevertheless, some innovations were introduced to render it more computationally efficient. We integrated this method into OpenFOAM, and applied it to typical examples with the same parameters as COMSOL Multiphysics, the output results were found to match almost completely with the latter. This method holds tremendous promise for practical application in battery design. It accurately represents chemical processes within the battery, including mass and charge transfer, migration and diffusion. Additionally, it improves efficiency over the full-order P2D model.