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.

翻译：基于连续介质理论，我们构建了一个瞬态多维多物理场模型，该模型耦合了锂离子电池充放电过程中同时发生的力学、热学和电化学现象。该过程产生一个耦合的非线性偏微分方程组。除初始条件和边界条件外，我们重点阐述了电极-电解质界面条件的处理，该条件对应于巴特勒-沃尔默反应动力学方程。我们给出了模型强形式和弱形式的推导，以及空间和时间上的离散化过程。离散化模型通过采用$hp$分层网格的有限元方法在二维空间中进行计算求解，并结合交错二阶半隐式时间积分。该方法的空间和时间误差估计均高于任何其他同类工作。针对典型电池单元几何结构，在不同运行场景下进行了仿真。数值结果表明，相较于仅考虑电化学耦合，完整模型能够提供更多重要的分析见解。随着充放电电流的增大，多物理场耦合的重要性愈发凸显。我们的完整模型为电池设计专业人员提供了优化设计、推动储能行业发展的宝贵工具。