Comparison of discretization methods applied to the single-particle model of lithium-ion batteries

A Modified Multiphysics model for Lithium-Ion batteries with a LixNi1/3Mn1/3Co1/3O2 electrode

“…Model extension is still ongoing. At the same time it is aimed to minimize the computational effort for instance by simplifying the diffusion equation in the solid phase [13][14][15]. Large efforts are focused on better assessing the impact of porosity and tortuosity of the electrodes and separator [16,6,7].…”

A Simplified Extension of Physics-Based Single Particle Model for Dynamic Discharge Current

“…Assuming that the temperature is constant in the SP model, then, the electrode potential is the function of the concentration of Li + ions in the intercalation particle of electrode. So, the terminal voltage V t is different between two electrode potentials and can be rewritten as [29] V…”

Computationally efficient approach for solving time dependent diffusion equation with discrete temporal convolution applied to granular particles of battery electrodes

“…The wavenumbers k n are chosen so that the eigen functions have zero derivative at granule surface: vJ n ðrÞ vr r¼R ¼ v r sinðk n rÞ k n r r¼R ¼ 0; (10) which is satisfied with the solutions of the transcendent equation: tanðk n RÞ ¼ k n R: (11) By choosing only eigen functions with zero derivative at the granule surface the boundary condition given by Equation (3) is met solely by the particular integral.…”

“…Presently, several methods are used to predict the surface concentration: finite difference method [11], finite element method [11,12], polynomial approximation [6,13], differential quadrature [11], Duhamel's superposition method [13], diffusion length method [13], analytical methods [8,14,15], pseudo steady state methods [13,14,16,17], orthogonal collocation on finite elements [5] and Pad e approximation state space method [4,18]. Results presented in Refs.…”

“…[11] this type of method enables achieving high accuracy of the concentration profile resolution. However, within the field of realtime capable battery models, the computational expenses of finite volume/differences methods mostly limit their application to only the single particle models [11].…”