### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 49-53 |

Number of pages | 5 |

Journal | Solid State Communications |

Volume | 296 |

DOIs | |

Publication status | Published - 1 Jul 2019 |

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### Keywords

- Analytical methods
- Porous electrodes
- Pseudo-steady state
- Spherical diffusion

### Cite this

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*Solid State Communications*, vol. 296, pp. 49-53. https://doi.org/10.1016/j.ssc.2019.04.011

**A modified pseudo-steady-state analytical expression for battery modeling.** / Chayambuka, K.; Mulder, G.; Danilov, D.L.; Notten, P.H.L. (Corresponding author).

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A modified pseudo-steady-state analytical expression for battery modeling

AU - Chayambuka, K.

AU - Mulder, G.

AU - Danilov, D.L.

AU - Notten, P.H.L.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - Analytical methods

KW - Porous electrodes

KW - Pseudo-steady state

KW - Spherical diffusion

UR - http://www.scopus.com/inward/record.url?scp=85065427220&partnerID=8YFLogxK

U2 - 10.1016/j.ssc.2019.04.011

DO - 10.1016/j.ssc.2019.04.011

M3 - Article

AN - SCOPUS:85065427220

VL - 296

SP - 49

EP - 53

JO - Solid State Communications

JF - Solid State Communications

SN - 0038-1098

ER -