# Numerical simulation of Li-ion battery thermo-electrochemical processes

• Zakharov Petr E., zapetch@gmail.com M. K. Ammosov North-Eastern Federal University, Mathematical and Computer Analysis Methods Scientiﬁc Laboratory, 42 Kulakovsky Street, Yakutsk 677891, Russia
• Nikiforova Marina A., lenni1937@gmail.com M. K. Ammosov North-Eastern Federal University, Mathematical and Computer Analysis Methods Scientiﬁc Laboratory, 42 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: Li-ion battery, thermo-electrochemical process, Butler-Volmer equation, finite element method

### Abstract

We present a numerical simulation of thermo-electrochemical processes of a Li-ion battery. Mathematical model of thermo-electrochemical processes is described on a microscopic scale and contains nonlinear equations for concentration, potential and temperature. A Li-ion battery consists of three subdomains: two electrodes and the electrolyte. On the interface of electrodes and electrolyte there are Lithium ions intercalation and deintercalation processes which are described by the Butler–Volmer nonlinear equation. The main problem of numerical implementation is the discontinuity of concentration and potential at the interface of the subdomains. To take into account the discontinuity, we use mixed finite elements in spatial approximation of a coupled system: discontinuous Galerkin elements for concentration and potential and continuous Galerkin elements for temperature. The time approximation is performed using a fully implicit scheme. The nonlinear system of equations obtained by approximation is solved by the Newton method.

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How to Cite
Zakharov, P. and Nikiforova, M. (&nbsp;) “Numerical simulation of Li-ion battery thermo-electrochemical processes”, Mathematical notes of NEFU, 25(4), pp. 102-114. doi: https://doi.org/10.25587/SVFU.2018.100.20557.
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Section
Mathematical Modeling