论文标题
来自最佳的传感器测量值的基于张量的流动重建
Tensor-based flow reconstruction from optimally located sensor measurements
论文作者
论文摘要
从稀疏测量中重建高分辨率流场是流体动力学的主要挑战。现有的方法通常通过将不同的空间方向彼此堆叠来矢量化流程，从而将不同维度编码的信息混淆。在这里，我们介绍了一种基于张量的传感器放置和流动重建方法，该方法保留并利用流动的固有多维性。我们得出了我们方法的流动重建误差，存储要求和计算成本的估计。我们以示例显示了我们的基于张量的方法比类似的矢量化方法明显更准确。此外，使用基于张量的方法时，误差的方差较小。尽管我们方法的计算成本与类似的矢量化方法相媲美，但它将存储成本降低了几个数量级。随着流量的尺寸增加，降低的存储成本变得更加明显。我们在三个例子上证明了我们方法的功效：混乱的Kolmogorov流动，原地和卫星测量全球海面温度，以及围绕海洋研究容器周围的3D不稳定模拟流。
Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in-situ and satellite measurements of the global sea surface temperature, and 3D unsteady simulated flow around a marine research vessel.
