An efficient 0D-space conservative and positivity preserving battery model
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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BibTeX
@misc{clain2026efficient,
title = {{An efficient 0D-space conservative and positivity preserving battery model}},
author = {S. Clain and M. C. Lucas and M. T. Malheiro and C. M. Costa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28121},
eprint = {2609.28121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28121},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An efficient 0D-space conservative and positivity preserving battery model
AU - S. Clain
AU - M. C. Lucas
AU - M. T. Malheiro
AU - C. M. Costa
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28121
UR - https://arxiv.org/abs/2609.28121
AB - 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.
ER -