多尺度传热的非侵入式混合方案：电池组中的热失控
Non-intrusive Hybrid Scheme for Multiscale Heat Transfer: Thermal Runaway in a Battery Pack
AI总结：
本文提出一种非侵入式双向耦合混合模型，结合细尺度与上尺度化方程，在限制计算成本的同时准确预测电池组热失控，并证明其计算效率优于细尺度模拟。
摘要：
多尺度系统的准确分析和数值建模是一项艰巨的任务。需要正确解析跨越多个数量级的空间和时间尺度，这挑战了我们的理论模型和计算能力的极限。严格的上尺度化技术能够实现高效计算，同时对误差进行限定/跟踪，并有助于做出明智的成本-精度权衡。最大的挑战出现在上尺度化模型的适用条件失效时。在此，我们提出了一种非侵入式双向（迭代自下而上与自上而下）耦合混合模型，应用于电池组中的热失控，该模型在同一数值模拟中结合了细尺度方程和上尺度化方程，以在限制计算成本的同时实现预测精度。首先，我们开发了两种不同精度阶的方法来强制耦合边界处的连续性。然后，我们推导了细尺度和上尺度化控制方程的弱（即变分）形式，以便在FEniCS中进行有限元（FE）离散化和数值实现。我们证明，混合模拟可以在由均匀化理论先验确定的误差界限内准确预测平均温度场。最后，我们展示了混合算法相对于细尺度模拟的计算效率。
英文摘要：
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 helping to make informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions of upscaled models break down. Here, we present a non-intrusive two-way (iterative bottom-up top-down) coupled hybrid model, applied to thermal runaway in battery packs, that combines fine-scale 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.
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