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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.
Spherical diffusion, Porous electrodes, Pseudo-steady state, Analytical methods, Spherical diffusion., Analytical methods, Pseudo-steady state, SDG 7 - Affordable and Clean Energy, info:eu-repo/classification/ddc/530, SDG 7 – Betaalbare en schone energie, Porous electrodes
Spherical diffusion, Porous electrodes, Pseudo-steady state, Analytical methods, Spherical diffusion., Analytical methods, Pseudo-steady state, SDG 7 - Affordable and Clean Energy, info:eu-repo/classification/ddc/530, SDG 7 – Betaalbare en schone energie, Porous electrodes
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 9 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |