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
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A modified pseudo-steady-state analytical expression for battery modeling. / Chayambuka, K.; Mulder, G.; Danilov, D.L.; Notten, P.H.L. (Corresponding author).
In: Solid State Communications, Vol. 296, 01.07.2019, p. 49-53.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 -