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The unified 3D phase-field model for the description of the lithium-ion cell as a whole is developed. The model takes into account the realistic distribution of particles in porous electrodes, percolative transport of ions, and the…
This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of…
The pseudo-two-dimensional (P2D) model is a complex mathematical model that can capture the electrochemical processes in Li-ion batteries. However, the model also brings a heavy computational burden. Many simplifications to the model have…
This paper investigates the state estimation of a high-fidelity spatially resolved thermal- electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations…
The widely used Doyler-Fuller-Newman (DFN) model for lithium-ion batteries is too computationally expensive for certain applications, which has motivated the appearance of a plethora of simpler models. These models are usually posed in an…
In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to…
The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit…
We present a simulation workflow for efficient investigations of the interplay between 3D lithium-ion electrode microstructures and electrochemical performance, with emphasis on lithium plating. Our approach addresses several challenges.…
Advanced battery management systems rely on mathematical models to guarantee optimal functioning of Lithium-ion batteries. The Pseudo-Two Dimensional (P2D) model is a very detailed electrochemical model suitable for simulations. On the…
The standard continuum model of a lithium-ion battery, the Doyle-Fuller-Newman (DFN) model, is computationally expensive to solve. Typically simpler models, such as the single particle model (SPM), are used to provide insight for control…
Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high…
In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis…
All solid state batteries are claimed to be the next-generation battery system, in view of their safety accompanied by high energy densities. A new advanced, multiscale compatible, and fully three dimensional model for solid electrolytes is…
We consider the mathematical treatment of a system of nonlinear partial differential equations based on a model, proposed in 1972 by J. Newman, in which the coupling between the Lithium concentration, the phase potentials and temperature in…
In this article we address the theoretical study of a multiscale drift-diffusion (DD) model for the description of photoconversion mechanisms in organic solar cells. The multiscale nature of the formulation is based on the co-presence of…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
This paper proposes physical-based, reduced-order electrochemical models that are much faster than the electrochemical pseudo 2D (P2D) model, while providing high accuracy even under the challenging conditions of high C-rate and strong…
This paper presents the Battery Modelling Toolbox (BattMo), a flexible finite volume continuum modelling framework in MATLAB\textsuperscript{\textregistered} (\citeproc{ref-MATLAB}{The MathWorks Inc., 2025}) for simulating the performance…
The Doyle-Fuller-Newman model is arguably the most ubiquitous electrochemical model in lithium-ion battery research. Since it is a highly nonlinear model, its input-output relations are still poorly understood. Researchers therefore often…
We investigate the modeling and simulation of ionic transport and charge conservation in lithium-ion batteries (LIBs) at the microscale. It is a multiphysics problem that involves a wide range of time scales. The associated computational…