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:准确地分析和数值建模多尺度系统是一项艰巨的任务。必须正确解析跨越数个数量级的空间和时间尺度,这既考验我们的理论模型,也挑战计算能力。严格的尺度提升技术可以实现高效计算,并限制/跟踪误差,同时进行明智的成本-准确性权衡。当尺度提升模型的适用条件破坏时,最大的挑战就出现了。在这里,我们提出了一个非侵入式的双向耦合混合模型,应用于电池组中的热失控,将精细和尺度提升方程结合在同一数值模拟中,以实现预测精度,同时限制计算成本。首先,我们开发了两种方法,具有不同的精度顺序,以在耦合边界处强制连续性。然后,我们为有限元(FE)离散化和在FEniCS中的数字实现,推导精细尺度和尺度提升控制方程的弱(即变分)公式。我们证明,混合模拟可以准确地预测平均温度场,误差边界由均匀化理论事先确定。最后,我们证明了混合算法相对于精细规模模拟的计算效率。