Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and making informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions for upscaled models break down. Here, we present a non-intrusive two-way coupled hybrid model, applied to thermal runaway in battery packs, that combines fine- and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.

翻译：多尺度系统的精确解析与数值建模是一项艰巨任务。为恰当解析跨越多个数量级的空间和时间尺度，既考验理论模型的极限，也挑战计算能力的边界。严格的上尺度技术能够实现高效计算，同时约束/追踪误差，并在成本与精度之间做出明智权衡。最大的挑战在于上尺度模型适用条件失效的情况。本文提出了一种非侵入式双向耦合混合模型，并将其应用于电池组热失控场景。该模型在同一数值模拟中结合了精细尺度方程与上尺度方程，既达到了预测精度，又限制了计算成本。首先，我们开发了两种不同精度阶次的方法来确保耦合边界上的连续性。随后，推导了精细尺度和上尺度控制方程的弱（变分）形式，用于有限元（FE）离散化及在FEniCS中的数值实现。我们证明，混合模拟能够准确预测平均温度场，其误差范围由均匀化理论预先确定。最后，我们通过与精细尺度模拟的对比，展示了混合算法的计算效率。