High-order transient multidimensional simulation of a thermo-electro-chemo-mechanical model for Lithium-ion batteries

We build a transient multidimensional multiphysical model based on continuum theories, involving the coupled mechanical, thermal and electrochemical phenomena occurring simultaneously in the discharge or charge of lithium-ion batteries. The process delivers a system of coupled nonlinear partial differential equations. Besides initial and boundary conditions, we highlight the treatment of the electrode-electrolyte interface condition, which corresponds to a Butler-Volmer reaction kinetics equation. We present the derivation of the strong and weak forms of the model, as well as the discretization procedure in space and in time. The discretized model is computationally solved in two dimensions by means of a finite element method that employs $hp$ layered meshes, along with staggered second order semi-implicit time integration. The expected error estimate is of higher order than any other similar work, both in space and in time. A representative battery cell geometry, under distinct operating scenarios, is simulated. The numerical results show that the full model allows for important additional insights to be drawn than when caring only for the electrochemical coupling. Considering the multiphysics becomes more important as the applied current is increased, whether for discharge or for charge. Our full model provides battery design professionals with a valuable tool to optimize designs and advance the energy storage industry.