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arXiv · 2609.28121

An efficient 0D-space conservative and positivity preserving battery model

S. Clain·M. C. Lucas·M. T. Malheiro·C. M. Costa
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Abstract

Embedded software aims to provide the main characteristics of a cell in real time to manage and optimize battery usage. A complete multidimensional model is not tractable with the low computational resources available in-situ. A class of 0D-in-space models is derived from the P2D Doyle-Fuller-Newman system, with additional assumptions about the functions' shape in space, and strongly reduces the complexity while preserving the main characteristics over time. We propose a conservative, positivity-preserving model built from the P2D system based on the statement that the Butler-Volmer source term is constant in each subdomain (anode, separator, cathode). We develop a mathematically rigorous construction that provides the simplified model and design a scheme to solve the system. We highlight that the model guaranties the conservation property together with the positivity of the concentrations. In particular, the diffusion-limited current density that represents the maximum current that can be used while still preserving the positivity of the cation concentration is obtained explicitly.

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S. Clain, M. C. Lucas, M. T. Malheiro, C. M. Costa. 2026-09-23. An efficient 0D-space conservative and positivity preserving battery model. https://arxiv.org/abs/2609.28121

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