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# A modified pseudo-steady-state analytical expression for battery modeling

Kudakwashe Chayambuka; Grietus Mulder; Dmitri L. Danilov; Prof. Peter H. L. Notten

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{
"description": "<p>The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS) method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS) expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS) expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.</p>",
"creator": [
{
"affiliation": "VITO, Boeretang 200, 2400 Mol, Belgium; EnergyVille, Thor Park 8310, 3600 Genk, Belgium; Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, Netherlands",
"@type": "Person",
"name": "Kudakwashe Chayambuka"
},
{
"affiliation": "VITO, Boeretang 200, 2400 Mol, Belgium; EnergyVille, Thor Park 8310, 3600 Genk, Belgium",
"@type": "Person",
"name": "Grietus Mulder"
},
{
"affiliation": "Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, Netherlands; Forschungszentrum J\u00fclich (IEK-9), D-52425 J\u00fclich, Germany",
"@type": "Person",
"name": "Dmitri L. Danilov"
},
{
"affiliation": "Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, Netherlands; Forschungszentrum J\u00fclich (IEK-9), D-52425 J\u00fclich, Germany; University of Technology Sydney, Broadway, Sydney, NSW 2007, Australia",
"@type": "Person",
"name": "Prof. Peter H. L. Notten"
}
],
"datePublished": "2019-04-24",
"url": "https://zenodo.org/record/3253470",
"keywords": [
"Porous electrodes, Pseudo-steady state, Analytical methods, Spherical diffusion."
],
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.1016/j.ssc.2019.04.011",
"@id": "https://doi.org/10.1016/j.ssc.2019.04.011",
"@type": "ScholarlyArticle",
"name": "A modified pseudo-steady-state analytical expression for battery modeling"
}
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