Finite Volume Discretization of Equations Describing Nonlinear Diffusion in Li-Ion Batteries

Popov, Peter; Vutov, Yavor; Margenov, Svetozar; Iliev, Oleg

doi:10.1007/978-3-642-18466-6_40

Cited by 15 publications

(20 citation statements)

References 3 publications

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“…Detailed results will be presented in [18]. Numerical algorithm for the introduced here model, as well as its numerical study for 3D geometry, are presented in [19]…”

Section: Discussionmentioning

confidence: 99%

Modeling of Species and Charge Transport in Li–Ion Batteries Based on Non-equilibrium Thermodynamics

Latz

Zausch

Iliev

2011

Numerical Methods and Applications

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In order to improve the design of Li ion batteries the complex interplay of various physical phenomena in the active particles of the electrodes and in the electrolyte has to be balanced. The separate transport phenomena in the electrolyte and in the active particle as well as their coupling due to the electrochemical reactions at the interfaces between the electrode particles and the electrolyte will influence the performance and the lifetime of a battery. Any modeling of the complex phenomena during the usage of a battery has therefore to be based on sound physical and chemical principles in order to allow for reliable predictions for the response of the battery to changing load conditions. We will present a modeling approach for the transport processes in the electrolyte and the electrodes based on non-equilibrium thermodynamics and transport theory. The assumption of local charge neutrality, which is known to be valid in concentrated electrolytes, is explicitly used to identify the independent thermodynamic variables and fluxes. The theory guarantees strictly positive entropy production. Differences to other theories will be discussed.

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“…Detailed results will be presented in [18]. Numerical algorithm for the introduced here model, as well as its numerical study for 3D geometry, are presented in [19]…”

Section: Discussionmentioning

confidence: 99%

Modeling of Species and Charge Transport in Li–Ion Batteries Based on Non-equilibrium Thermodynamics

Latz

Zausch

Iliev

2011

Numerical Methods and Applications

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“…Following [16], the continuous model is discretized using a basic cell centered finite volume scheme on a voxel grid. Each voxel is assigned a unique subdomain and the Butler-Volmer conditions are chosen as numerical flux on grid faces separating an electrolyte from an electrode voxel.…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry

Ohlberger

Rave

2017

Model Reduction of Parametrized Systems

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In this contribution we present first results towards localized model order reduction for spatially resolved, three-dimensional lithium-ion battery models. We introduce a localized reduced basis scheme based on non-conforming local approximation spaces stemming from a finite volume discretization of the analytical model and localized empirical operator interpolation for the approximation of the model's nonlinearities. Numerical examples are provided indicating the feasibility of our approach.

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“…With these choices (2.1) can be seen as a generalization of a mathematical model for lithium ion batteries; see, e.g., [10,22,25]. ♦ Remark 2.1.…”

Section: The Nonlinear Elliptic-parabolic Systemmentioning

confidence: 99%

“…These coupled system can be viewed as a generalization of a mathematical model for lithium ion batteries; see, e.g., [10,22,25]. The parabolic equation describes the concentration of lithium ions and the two elliptic PDEs model the potential in the solid and liquid phase, respectively.…”

Section: Introductionmentioning

confidence: 99%

POD Galerkin Schemes for Nonlinear Elliptic-Parabolic Systems

Lass¹,

Volkwein²

2013

SIAM J. Sci. Comput.

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Abstract. In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system and its POD approximation. The nonlinear coupling is realized by variants of the empirical interpolation introduced by Barrault et al. [3] and Chaturantabut et al. [4]. Numerical examples illustrate the efficiency of the proposed reduced-order modeling.

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Finite Volume Discretization of Equations Describing Nonlinear Diffusion in Li-Ion Batteries

Cited by 15 publications

References 3 publications

Modeling of Species and Charge Transport in Li–Ion Batteries Based on Non-equilibrium Thermodynamics

Modeling of Species and Charge Transport in Li–Ion Batteries Based on Non-equilibrium Thermodynamics

Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry

POD Galerkin Schemes for Nonlinear Elliptic-Parabolic Systems

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